Question:
Let A=\(\begin{pmatrix} 0&0 &1 \\ 1&0 &0 \\ 0&0 &0 \end{pmatrix}\), B=\(\begin{pmatrix} 0&1 &0 \\ 0&0 &1 \\ 0&0 &0 \end{pmatrix}\) and P=\(\begin{pmatrix} 0&1 &0 \\ x&0 &0 \\ 0&0 &y \end{pmatrix}\) be an orthogonal matrix such that B=PAP-1 holds. Then
Let A=\(\begin{pmatrix} 0&0 &1 \\ 1&0 &0 \\ 0&0 &0 \end{pmatrix}\), B=\(\begin{pmatrix} 0&1 &0 \\ 0&0 &1 \\ 0&0 &0 \end{pmatrix}\) and P=\(\begin{pmatrix} 0&1 &0 \\ x&0 &0 \\ 0&0 &y \end{pmatrix}\) be an orthogonal matrix such that B=PAP-1 holds. Then
Updated On: Dec 13, 2024
- x-1=y
- x=1,y=0
- x=0,y=1
- x=-1,y=0
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The Correct Option is A
Solution and Explanation
The correct answer is option (A): x-1=y
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Concepts Used:
Matrix Transformation
The numbers or functions that are kept in a matrix are termed the elements or the entries of the matrix.
Transpose Matrix:
The matrix acquired by interchanging the rows and columns of the parent matrix is termed the Transpose matrix. The definition of a transpose matrix goes as follows - “A Matrix which is devised by turning all the rows of a given matrix into columns and vice-versa.”