Test: Elementary Operations


5 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Elementary Operations


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QUESTION: 1

To check whether the matrix B is an inverse of matrix A, we need to check whether​

Solution:

An n×n matrix A is said to be invertible if there exists an n×n matrix B such that AB=I, and BA=I, where I is the n×n identity matrix.
If such a matrix B exists, then it is known to be unique and called the inverse matrix of A, denoted by A−1.

QUESTION: 2

The inverse of a matrix is defined for

Solution:

The inverse exists only for square matrix. However this is not true. A nonsingular matrix must have their inverse whether it is square or nonsquare matrix.

QUESTION: 3

The inverse of   is

Solution:

A = IA
AA-1 = I
A = {(1,0),(-1,1)}
A-1{(1,0),(-1,1)} =  {(1,0),(0,1)}
R2 ----> R2 + R1
A^-1 {(1,0),(0,1)} = {(1,0),(1,1)}
I A-1 = {(1,0),(1,1)}
Therefore, A-1 = {(1,0),(1,1)}

QUESTION: 4

The inverse of   is

Solution:

A = {(0,1) (1,0)}
Adj(A) = {(0,(-1)) ((-1),0)}
|A| = (0 - 1) = -1
A-1 = adj(A)/|A|
= -1{(0,(-1)) ((-1),0)}
= {(0,1) (1,0)}

QUESTION: 5

If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A​

Solution:

ANSWER :- a

Solution :- Matrix equivalence is an equivalence relation on the space of rectangular matrices.

For two rectangular matrices of the same size, their equivalence can also be characterized by the following conditions

  • The matrices can be transformed into one another by a combination of elementary row and column operations.

If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be equivalent of A.​