Question
Download Solution PDFIf \(\begin{bmatrix} 1 & -3 & 2 \\\ 2 & -8 & 5 \\\ 4 & 2 & λ \end{bmatrix}\) is not an invertible matrix, then what is the value of λ ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If the matrix A is not an invertible matrix then | A | = 0
If the matrix A is the non-singular matrix then | A | ≠ 0
Calculations:
Given, A = \(\begin{bmatrix} 1 & -3 & 2 \\\ 2 & -8 & 5 \\\ 4 & 2 & λ \end{bmatrix}\)is not an invertible matrix
As we know, If the matrix A is non invertible matrix then | A | = 0
⇒ \(\begin{vmatrix} 1 & -3 & 2 \\\ 2 & -8 & 5 \\\ 4 & 2 & λ \end{vmatrix}\) = 0
⇒ 1\(\rm (-8\lambda - 10)+3(2\lambda-20)+2(4+32)\) = 0
⇒ \(\rm -8\lambda - 10+6\lambda-60+72 = 0\)
⇒\(\rm -2\lambda +2 = 0\)
⇒\(\rm \lambda = 1\)
Hence, If \(\begin{bmatrix} 1 & -3 & 2 \\\ 2 & -8 & 5 \\\ 4 & 2 & λ \end{bmatrix}\) is not an invertible matrix, then the value of λ is 1.
Last updated on Jun 11, 2025
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