Question:
Let \(\beta\) be a real number. Consider the matrix
\(A=\begin{pmatrix}\beta & 0 & 1 \\2 & 1 & -2 \\3 & 1 & -2\end{pmatrix}\)
If \(A^7-(\beta-1) A^6-\beta A^5\) is a singular matrix, then the value of \(9 \beta\) is __.
Let \(\beta\) be a real number. Consider the matrix
\(A=\begin{pmatrix}\beta & 0 & 1 \\2 & 1 & -2 \\3 & 1 & -2\end{pmatrix}\)
If \(A^7-(\beta-1) A^6-\beta A^5\) is a singular matrix, then the value of \(9 \beta\) is __.
\(A=\begin{pmatrix}\beta & 0 & 1 \\2 & 1 & -2 \\3 & 1 & -2\end{pmatrix}\)
If \(A^7-(\beta-1) A^6-\beta A^5\) is a singular matrix, then the value of \(9 \beta\) is __.
Updated On: Apr 23, 2024
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Correct Answer: 3
Solution and Explanation
The answer is 3.
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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.