Question:
If $O(A) = 2 \times 3, O (B) = 3 \times 2$, and $O(C) = 3 \times 3$, which one of the following is not defined.
If $O(A) = 2 \times 3, O (B) = 3 \times 2$, and $O(C) = 3 \times 3$, which one of the following is not defined.
Updated On: Jul 29, 2024
- $C(A+B')$
- $C(A+B')'$
- $BAC$
- $CB+A'$
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The Correct Option is A
Solution and Explanation
Given that $O\left(A\right) = 2 \times3 , O\left(B\right) = 3\times 2 $ and $ O\left(C\right) = 3 \times3 $
$ \Rightarrow \, O\left(A'\right) = 3 \times2 , O\left(B'\right) = 2\times 3$
(a) $CB+A' $
Now order of CB = (order of C) (order of B)
= (order of C is $3 \times 3$) (order of B is $3 \times 2$)
= order of CB is $3 \times 2$
Since $O(A' ) = 3 \times 2$
$\therefore$ Matrix CB + A' can be determined.
(b) $O(BA) = 3 \times 3$
and $O(C) = 3 \times 3$
$\therefore$ Matrix BAC can be determined.
(c) $C(A + B')'$
$O(A + B') = 2 \times 3$
$\Rightarrow \; O(A + B')' = 3 \times 2$
and $O(C) = 3 \times 3$
$\therefore$ Matrix $C(A + B')'$ can be determined.
(d) $C(A + B')$
$O(A + B') = 2 \times 3$
and $O(C) = 3 \times 3$
$\therefore$ Matrix $C (A + B')$ cannot be determined
$ \Rightarrow \, O\left(A'\right) = 3 \times2 , O\left(B'\right) = 2\times 3$
(a) $CB+A' $
Now order of CB = (order of C) (order of B)
= (order of C is $3 \times 3$) (order of B is $3 \times 2$)
= order of CB is $3 \times 2$
Since $O(A' ) = 3 \times 2$
$\therefore$ Matrix CB + A' can be determined.
(b) $O(BA) = 3 \times 3$
and $O(C) = 3 \times 3$
$\therefore$ Matrix BAC can be determined.
(c) $C(A + B')'$
$O(A + B') = 2 \times 3$
$\Rightarrow \; O(A + B')' = 3 \times 2$
and $O(C) = 3 \times 3$
$\therefore$ Matrix $C(A + B')'$ can be determined.
(d) $C(A + B')$
$O(A + B') = 2 \times 3$
and $O(C) = 3 \times 3$
$\therefore$ Matrix $C (A + B')$ cannot be determined
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Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
- Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.