If \(\begin{bmatrix} 1 & -3 & 2 \\\ 2 & -8 & 5 \\\ 4 & 2 & λ \end{bmatrix}\) is not an invertible matrix, then what is the value of λ ?
1. -1
2. 0
3. 1
4. 2
1. -1
2. 0
3. 1
4. 2
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Correct Answer – Option 3 : 1
Concept:
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.