Question:
If $A$ is $3 \times 4$ matrix and $B$ is a matrix such that $A'B$ and $BA'$ are both defined. Then $B$ is of the type
If $A$ is $3 \times 4$ matrix and $B$ is a matrix such that $A'B$ and $BA'$ are both defined. Then $B$ is of the type
Updated On: Apr 2, 2024
- $3 \times 4$
- $4\times 3$
- $3 \times 3$
- $4 \times 4$
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The Correct Option is A
Solution and Explanation
Given, $A$ is $3 \times 4$ matrix.
So, $A'$ is $4 \times 3$ matrix.
Since, $A' B$ is defined, therefore $B$ should he $3 \times 4.$
Also, $B A'$ is defined, so $B$ should be $3 \times 4$.
Hence, $B$ is of the type $3 \times 4$
So, $A'$ is $4 \times 3$ matrix.
Since, $A' B$ is defined, therefore $B$ should he $3 \times 4.$
Also, $B A'$ is defined, so $B$ should be $3 \times 4$.
Hence, $B$ is of the type $3 \times 4$
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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.