If A = diag [ 5 -2 7] ; B = diag [7 8 5], then 3A - 2B is ____.

Correct! Wrong!

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3A = diag [15 -6 21] 2B = diag [14 16 10] 3A - 2B = diag [15 -6 21] - diag [14 16 10] = diag [1 -22 11]

The total number of elements in a matrix represents a prime number. The possible orders the matrix can have is _____.

Correct! Wrong!

The possible orders it can have is 2. As prime numbers have exactly two factors, only two orders are possible. For, example, 5 is a prime number. The orders possible are 5 × 1 and 1 × 5.

Given a matrix A = [aij]; 2 ≤ i ≤ 4and 3 ≤ j ≤ 5 where aij = i + 2j; the elements a23 and a36 are ______.

Correct! Wrong!

The elements a23 and a36 are 8 and 'not defined'. a23 : => i = 2 => j = 3 i + 2j = 8 a36 : j = 6 , However, 3 ≤ j ≤ 5, which will not be satisfied. Therefore, a36 is not defined.

The addition of constant multiplication of the elements of any row to the corresponding element of any other row is denoted by __________________.

Correct! Wrong!

The addition of the elements of ith row with the corresponding elements of jth row, multiplied by k is denoted by Ri → Ri + kRj.

If A and B are invertible matrices of the same order, then (AB)-1= _______________.

Correct! Wrong!

If A and B are invertible matrices of the same order, then (AB)-1 = B-1 A-1. Let A and B be invertible matrices of the same order, then (AB)( AB)-1= I (by definition of inverse of a matrix) Pre-multiplying by A-1, A-1 (AB)(AB)-1 = A-1I => (A-1A) B(AB)-1 = A-1 (A-1I = A-1) => I B(AB)-1 = A-1 => B(AB)-1 = A-1 Pre-multiplying by B-1 => (B-1B) (AB)-1 = B-1A-1 => I (AB)-1 = B-1A-1 Therefore, (AB)-1 = B-1A-1

If A is a symmetric matrix and n ε N, then An is ____.

Correct! Wrong!

AT = A (A is a symmetric matrix) (AT)n = An ⇨ (An)T = An Hence An is a symmetric matrix.

The interchange of any two rows is given by ___________.

Correct! Wrong!

If the ith and jth rows are interchanged, then this transformation is indicated by Ri ↔ Rj.

The number of elementary operations on a matrix are __________.

Correct! Wrong!

There are 6 operations on a matrix, 3 of which are due to rows and 3 due to columns. These operations are known as elementary transformations. 1 The interchange of any two rows or columns. 2 The multiplication of the elements of any row or column by a non-zero number. 3 The addition to the elements of any row or column, the corresponding elements of any other row or column multiplied by any non-zero number.

If X is any m × n matrix such that XY and YX both defined, then Y is an ____.

Correct! Wrong!

If XY is defined, then the number of rows of Y should be n and if YX is defined, then the number of columns of matrix Y should be m. Therefore, Y should be a matrix of order n × m.

The elementary transformation ____________ is not possible on a matrix.

Correct! Wrong!

The elementary transformation C1 → 3C2is not possible on a matrix. The multiplication of each element of the ith column by k, where k ≠ 0 is given by Ci → kCi. Therefore, C1 → 3C1 is possible but C1 → 3C2is not possible. C1 → 3C1 is possible but C1 → 3C2

If A is a symmetric matrix of integers with zeroes on the main diagonal, the sum of the entries of A must be an ____.

Correct! Wrong!

The sum of the entries of A must be an even integer. If sum of the entries of A is not an even integer, matrix A cannot be a symmetric matrix.

If A = [aij] is a skew-symmetric matrix of order n, then aii is equal to ____.

Correct! Wrong!

If A [aij] is a skew-symmetric matrix, aii is equal to 0. Hence, aii is equal to 0 for all i = 1, 2 ...n.

Inverse of a square matrix, if it exists, is ________________.

Correct! Wrong!

Inverse of a square matrix, if it exists, is unique. Let A be a square matrix of order 'k'. If possible, let B and C be two inverses of A. Since B is the inverse of A, AB = BA = I. As C is the inverse of A, AC = CA = I. Then, B = BI = B (AC) = (BA) C = IC = C => Inverse of a square matrix, if it exists, is unique.

The inverse of a symmetric matrix is ____.

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The inverse of a symmetric matrix is also a symmetric matrix.

In order to use elementary column operations, we write A = ___________.

Correct! Wrong!

In order to use elementary column operations, we write A = A = AI. If A is matrix such that A-1exists, then to find A-1using elementary column operations, we write A = AI and apply a sequence of column operations on A = AI, till we get I = AB.

If A is a square matrix of order p and if there exists another square matrix B of the same order p, such that AB = BA = I, then _________________.

Correct! Wrong!

If A is a square matrix of order p and if there exists another square matrix B of the same order p, such that AB = BA = I, then B is called the inverse matrix of A. If A = [aij] be a square matrix of order p. If B is another square matrix of the same order and AB = BA = I, then B is called the inverse matrix of A. It is denoted by A-1. A is said to be invertible. If B is the inverse of A, then A is also the inverse of B.

The order of the matrix [3 5 -7] is _____.

Correct! Wrong!

The order the matrix [3 5 -7] is 1 × 3 as there is only one row and 3 columns.

If A, B are symmetric matrices of the same order, then AB - BA is a ____.

Correct! Wrong!

A and B are symmetric matrices. Therefore, A' = A and B' = B (AB - BA)' = (AB)' - (BA)' = B'A' - A'B' = BA - AB (Since, A' = A and B' = B) = - (AB - BA) ⇨ AB - BA is skew - symmetric.

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CBSE Class 12th Math 3 - Matrices MCQs
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