Let A be a matrix of order 3×3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to ______.
\(512 × 10^6\)
\(256 × 10^6\)
\(1024 × 10^6\)
\(256 × 10^{11}\)
The Correct Option is A
Solution and Explanation
|A| = 2
||A| adj(5 adjA3)|
= |25|A| adj(adjA3)|
= 253 |A|3⋅ |adjA3|2
= 253⋅ 23⋅ |A3|4
= 253⋅ 23⋅ 212
= 106⋅ 512
= 512⋅106
So, the correct option is (A): 512 x 106
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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.