Maths-
General
Easy

Question

The value of x for which the matrix A = open square brackets table row 2 0 7 row 0 1 0 row 1 cell negative 2 end cell 1 end table close square brackets is inverse of B = open square brackets table row cell negative x end cell cell 14 x end cell cell 7 x end cell row 0 1 0 row x cell negative 4 x end cell cell negative 2 x end cell end table close square brackets is

  1. fraction numerator 1 over denominator 2 end fraction
  2. fraction numerator 1 over denominator 3 end fraction
  3. fraction numerator 1 over denominator 4 end fraction
  4. fraction numerator 1 over denominator 5 end fraction

The correct answer is: fraction numerator 1 over denominator 5 end fraction


    We have

    AB = open square brackets table row cell 5 x end cell 0 0 row 0 1 0 row 0 cell 10 x minus 2 end cell cell 5 x end cell end table close square brackets = open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets

    x = 1/5

    Related Questions to study

    General
    maths-

    The greatest possible difference between two of the roots if  theta element of  [0, 2straight pi] is

    The greatest possible difference between two of the roots if  theta element of  [0, 2straight pi] is

    maths-General
    General
    maths-

    Statement I : open square brackets table row 5 0 0 row 0 3 0 row 0 0 2 end table close square brackets is a diagonal matrix.
    Statement II : A square matrix A = (aij) is a diagonal matrix if aij = 0 .for all straight i times not equal to straight j

    Statement I : open square brackets table row 5 0 0 row 0 3 0 row 0 0 2 end table close square brackets is a diagonal matrix.
    Statement II : A square matrix A = (aij) is a diagonal matrix if aij = 0 .for all straight i times not equal to straight j

    maths-General
    General
    maths-

    Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity. Denote by tr(A), The sum of diagonal entries of A, Assume that A2 = I.
    Statement-I :If Anot equal toI and Anot equal to– I, then det  A= – 1
    Statement-II : If A not equal to I and A not equal to – I then tr(A)not equal to0.

    Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity. Denote by tr(A), The sum of diagonal entries of A, Assume that A2 = I.
    Statement-I :If Anot equal toI and Anot equal to– I, then det  A= – 1
    Statement-II : If A not equal to I and A not equal to – I then tr(A)not equal to0.

    maths-General
    parallel
    General
    maths-

    Suppose A equals open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets, B equals open square brackets table row 2 0 row 0 cell negative 2 end cell end table close square brackets let x be a 2×2 matrix such that X to the power of straight primeAX = B
    Statement-I : X is non singular & |x| = ±2
    Statement-II : X is a singular matrix

    Suppose A equals open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets, B equals open square brackets table row 2 0 row 0 cell negative 2 end cell end table close square brackets let x be a 2×2 matrix such that X to the power of straight primeAX = B
    Statement-I : X is non singular & |x| = ±2
    Statement-II : X is a singular matrix

    maths-General
    General
    maths-

    If 2 tan invisible function application A equals 3 tan invisible function application B comma then fraction numerator sin invisible function application 2 B over denominator 5 minus cos invisible function application 2 B end fractionis equal to

    If 2 tan invisible function application A equals 3 tan invisible function application B comma then fraction numerator sin invisible function application 2 B over denominator 5 minus cos invisible function application 2 B end fractionis equal to

    maths-General
    General
    maths-

    Statement-I : If A & B are two 3×3 matrices such that AB = 0, then A = 0 or B = 0
    Statement-II : If A, B & X are three 3×3 matrices such that AX = B, |A| not equal to0, then X = A–1B

    Statement-I : If A & B are two 3×3 matrices such that AB = 0, then A = 0 or B = 0
    Statement-II : If A, B & X are three 3×3 matrices such that AX = B, |A| not equal to0, then X = A–1B

    maths-General
    parallel
    General
    maths-

    Assertion (A): The inverse of the matrix open square brackets table row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets does not exist.
    Reason (R) : The matrix open square brackets table row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets is singular. [becauseopen vertical bar table row 1 3 5 row 2 6 10 row 9 8 7 end table close vertical bar = 0, since R2 = 2R1]

    Assertion (A): The inverse of the matrix open square brackets table row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets does not exist.
    Reason (R) : The matrix open square brackets table row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets is singular. [becauseopen vertical bar table row 1 3 5 row 2 6 10 row 9 8 7 end table close vertical bar = 0, since R2 = 2R1]

    maths-General
    General
    maths-

    Assertion (A): open square brackets table row 5 0 0 row 0 3 0 row 0 0 9 end table close square brackets is a diagonal matrix
    Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i not equal to j.

    Assertion (A): open square brackets table row 5 0 0 row 0 3 0 row 0 0 9 end table close square brackets is a diagonal matrix
    Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i not equal to j.

    maths-General
    General
    maths-

    Consider open vertical bar table row cell a subscript 1 end subscript end cell cell b subscript 1 end subscript end cell cell c subscript 1 end subscript end cell row cell a subscript 2 end subscript end cell cell b subscript 2 end subscript end cell cell c subscript 2 end subscript end cell row cell a subscript 3 end subscript end cell cell b subscript 3 end subscript end cell cell c subscript 3 end subscript end cell end table close vertical bar= – 1, where ai. aj + bi. bj + ci.cj = open square brackets table row cell 0 semicolon end cell cell i not equal to j end cell row cell 1 semicolon end cell cell i equals j end cell end table close and i, j = 1,2,3
    Assertion(A) : The value of open vertical bar table row cell a subscript 1 end subscript plus 1 end cell cell b subscript 1 end subscript end cell cell c subscript 1 end subscript end cell row cell a subscript 2 end subscript end cell cell b subscript 2 end subscript plus 1 end cell cell c subscript 2 end subscript end cell row cell a subscript 3 end subscript end cell cell b subscript 3 end subscript end cell cell c subscript 3 end subscript plus 1 end cell end table close vertical bar is equal to zero
    Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0

    Consider open vertical bar table row cell a subscript 1 end subscript end cell cell b subscript 1 end subscript end cell cell c subscript 1 end subscript end cell row cell a subscript 2 end subscript end cell cell b subscript 2 end subscript end cell cell c subscript 2 end subscript end cell row cell a subscript 3 end subscript end cell cell b subscript 3 end subscript end cell cell c subscript 3 end subscript end cell end table close vertical bar= – 1, where ai. aj + bi. bj + ci.cj = open square brackets table row cell 0 semicolon end cell cell i not equal to j end cell row cell 1 semicolon end cell cell i equals j end cell end table close and i, j = 1,2,3
    Assertion(A) : The value of open vertical bar table row cell a subscript 1 end subscript plus 1 end cell cell b subscript 1 end subscript end cell cell c subscript 1 end subscript end cell row cell a subscript 2 end subscript end cell cell b subscript 2 end subscript plus 1 end cell cell c subscript 2 end subscript end cell row cell a subscript 3 end subscript end cell cell b subscript 3 end subscript end cell cell c subscript 3 end subscript plus 1 end cell end table close vertical bar is equal to zero
    Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0

    maths-General
    parallel
    General
    maths-

    Assertion(A) : The inverse of the matrix A = [Aij]n × n where aij = 0, i greater or equal than j is B = [aij–1]n× n 
    Reason(R): The inverse of singular matrix does not exist

    Assertion(A) : The inverse of the matrix A = [Aij]n × n where aij = 0, i greater or equal than j is B = [aij–1]n× n 
    Reason(R): The inverse of singular matrix does not exist

    maths-General
    General
    maths-

    Assertion : The product of two diagonal matrices of order 3 × 3 is also a diagonal matrix
    Reason : matrix multiplicationis non commutative

    Assertion : The product of two diagonal matrices of order 3 × 3 is also a diagonal matrix
    Reason : matrix multiplicationis non commutative

    maths-General
    General
    maths-

    Assertion : If A is a skew symmetric of order 3 then its determinant should be zero.
    Reason : If A is square matrix then det A = det straight A to the power of straight prime = det (–straight A to the power of straight prime)

    Assertion : If A is a skew symmetric of order 3 then its determinant should be zero.
    Reason : If A is square matrix then det A = det straight A to the power of straight prime = det (–straight A to the power of straight prime)

    maths-General
    parallel
    General
    maths-

    Assertion : There are only finitely many 2 × 2 matrices which commute with the matrix open square brackets table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets
    Reason : If A is non-singular then it commutes with I, adj A and A–1

    Assertion : There are only finitely many 2 × 2 matrices which commute with the matrix open square brackets table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets
    Reason : If A is non-singular then it commutes with I, adj A and A–1

    maths-General
    General
    Maths-

    Statement-I The equation square root of 3 cos space x minus sin space x equals 2 has exactly one solution in [0, 2straight pi].

    Statement-II For equations of type a cos space theta plus b sin space theta equals c to have real solutions in left square bracket 0 comma 2 pi right square bracket comma vertical line c vertical line less or equal than square root of a squared plus b squared end root  should hold true.

    In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not , is same like assertion and reason. Here, Start solving first Statement and try to prove it . Then solve the Statement-II . Remember cos a cosb -sin a sinb = cos ( a + b ) and sin a cosb + cosa sinb = sin( a+ b) .

    Statement-I The equation square root of 3 cos space x minus sin space x equals 2 has exactly one solution in [0, 2straight pi].

    Statement-II For equations of type a cos space theta plus b sin space theta equals c to have real solutions in left square bracket 0 comma 2 pi right square bracket comma vertical line c vertical line less or equal than square root of a squared plus b squared end root  should hold true.

    Maths-General

    In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not , is same like assertion and reason. Here, Start solving first Statement and try to prove it . Then solve the Statement-II . Remember cos a cosb -sin a sinb = cos ( a + b ) and sin a cosb + cosa sinb = sin( a+ b) .

    General
    maths-

    Assertion : If A is a skew symmetric matrix of order 3 then its determinant should be zero.
    Reason : If A is square matrix then det A = det straight A to the power of straight prime  = det (–straight A to the power of straight prime)

    Assertion : If A is a skew symmetric matrix of order 3 then its determinant should be zero.
    Reason : If A is square matrix then det A = det straight A to the power of straight prime  = det (–straight A to the power of straight prime)

    maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.