Maths-
General
Easy
Question
Matrix [1 2]
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](data:image/png;base64,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)
= [1 2]
= [1 2] ![open square brackets table row 8 row 7 end table close square brackets](data:image/png;base64,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)
= [8 + 14] = [2 2]
Related Questions to study
maths-
If A –2B =
and 2A – 3B =
, then matrix B is equal to–
If A –2B =
and 2A – 3B =
, then matrix B is equal to–
maths-General
maths-
The value of x for which the matrix A =
is inverse of B =
is
The value of x for which the matrix A =
is inverse of B =
is
maths-General
maths-
The greatest possible difference between two of the roots if [0, 2
] is
The greatest possible difference between two of the roots if [0, 2
] is
maths-General
maths-
Statement I :
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](data:image/png;base64,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)
Statement I :
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](data:image/png;base64,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)
maths-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 A
I and A
– I, then det A= – 1
Statement-II : If A
I and A
– I then tr(A)
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
I and A
– I, then det A= – 1
Statement-II : If A
I and A
– I then tr(A)
0.
maths-General
maths-
Suppose
,
let x be a 2×2 matrix such that
AX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix
Suppose
,
let x be a 2×2 matrix such that
AX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix
maths-General
maths-
If
then
is equal to
If
then
is equal to
maths-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|
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|
0, then X = A–1B
maths-General
maths-
Assertion (A): The inverse of the matrix
does not exist.
Reason (R) : The matrix
is singular. [![because](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACRJREFUeNpjYMAE/6EYGwiAyi1nIACoYsgoIAzwBTR9DaEPAABHCgvlC8PdSAAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIzNTs8L21vPjwvbWF0aD6HYN/sAAAAAElFTkSuQmCC)
= 0, since R2 = 2R1]
Assertion (A): The inverse of the matrix
does not exist.
Reason (R) : The matrix
is singular. [![because](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACRJREFUeNpjYMAE/6EYGwiAyi1nIACoYsgoIAzwBTR9DaEPAABHCgvlC8PdSAAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIzNTs8L21vPjwvbWF0aD6HYN/sAAAAAElFTkSuQmCC)
= 0, since R2 = 2R1]
maths-General
maths-
Assertion (A):
is a diagonal matrix
Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i
j.
Assertion (A):
is a diagonal matrix
Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i
j.
maths-General
maths-
Consider
= – 1, where ai. aj + bi. bj + ci.cj =
and i, j = 1,2,3
Assertion(A) : The value of
is equal to zero
Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0
Consider
= – 1, where ai. aj + bi. bj + ci.cj =
and i, j = 1,2,3
Assertion(A) : The value of
is equal to zero
Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0
maths-General
maths-
Assertion(A) : The inverse of the matrix A = [Aij]n × n where aij = 0, i
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
j is B = [aij–1]n× n
Reason(R): The inverse of singular matrix does not exist
maths-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
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
= det (–
)
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
= det (–
)
maths-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](data:image/png;base64,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)
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](data:image/png;base64,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)
Reason : If A is non-singular then it commutes with I, adj A and A–1
maths-General