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 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

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.

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.

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.

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.

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.

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.

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 inverse of a symmetric matrix is ____.

Correct! Wrong!

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

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

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.

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.

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, 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.

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.

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CBSE Class 12th Math 3 - Matrices MCQs
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