Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Matrix [1 2] $open parentheses open square brackets table row cell negative 2 end cell 5 row 3 2 end table close square brackets open square brackets table row 1 row 2 end table close square brackets close parentheses$ is equal to-

[1 2 2]
[2 3]
[2 2]
None of these

The correct answer is: [2 2]

We have
[1 2] $open parentheses open square brackets table row cell negative 2 end cell 5 row 3 2 end table close square brackets open square brackets table row 1 row 2 end table close square brackets close parentheses$
= [1 2] $open square brackets table row cell negative 2 plus 10 end cell row cell 3 plus 4 end cell end table close square brackets$ = [1 2] $open square brackets table row 8 row 7 end table close square brackets$
= [8 + 14] = [2 2]

Related Questions to study

If A –2B = $open square brackets table row 1 5 row 3 7 end table close square brackets$ and 2A – 3B = $open square brackets table row cell negative 2 end cell 5 row 0 7 end table close square brackets$ , then matrix B is equal to–

If A –2B = $open square brackets table row 1 5 row 3 7 end table close square brackets$ and 2A – 3B = $open square brackets table row cell negative 2 end cell 5 row 0 7 end table close square brackets$ , then matrix B is equal to–

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

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

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

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

parallel

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 . $for all straight i times not equal to straight j$

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 A $not equal to$ I and A $not equal to$ – I, then det A= – 1
Statement-II : If A $not equal to$ I and A $not equal to$ – I then tr(A) $not equal to$ 0.

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 A $not equal to$ I and A $not equal to$ – I, then det A= – 1
Statement-II : If A $not equal to$ I and A $not equal to$ – I then tr(A) $not equal to$ 0.

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 $X to the power of straight prime$ AX = 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 $X to the power of straight prime$ AX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix

parallel

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

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

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| $not equal to$ 0, 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| $not equal to$ 0, then X = A^–1B

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. [ $because$ $open vertical bar table row 1 3 5 row 2 6 10 row 9 8 7 end table close vertical bar$ = 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. [ $because$ $open vertical bar table row 1 3 5 row 2 6 10 row 9 8 7 end table close vertical bar$ = 0, since R₂ = 2R₁]

parallel

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 = (a_ij) is a diagonal matrix if a_ij = 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 = (a_ij) is a diagonal matrix if a_ij = 0 for all i $not equal to$ j.

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 a_i. a_j + b_i. b_j + c_i.c_j = $open square brackets table row cell 0 semicolon end cell cell i not equal to j end cell row cell 1 semicolon end cell cell i equals j end cell end table close$ 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 AA^T = 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 a_i. a_j + b_i. b_j + c_i.c_j = $open square brackets table row cell 0 semicolon end cell cell i not equal to j end cell row cell 1 semicolon end cell cell i equals j end cell end table close$ 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 AA^T = I, then | A + I | = 0

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

parallel

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

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 (– $straight A to the power of straight prime$ )

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

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.