The matrix 5103-2-46-1-2 b is a singular matrix- if the value of b isa -3b 3c 0d non-existent

(d) non existent For any singular matrix, the value of the determinant is 0. Here, A=5103 2 46 1 2bA=5( 4b+12) 10( 2b+6)+3(4 4)=0 #8658; 20b+60+20b 12=0 Hen ...

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Standard XII

Mathematics

Inverse of a Matrix

The matrix 51...

Question

The matrix $[\begin{matrix} 5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b \end{matrix}]$ is a singular matrix, if the value of b is
(a) − 3
(b) 3
(c) 0
(d) non-existent

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Solution

(d) non-existent
For any singular matrix, the value of the determinant is 0.
Here,

$A = [\begin{matrix} 5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b \end{matrix}] |A| = 5 (- 4 b + 12) - 10 (- 2 b + 6) + 3 (4 - 4) = 0 \Rightarrow - 20 b + 60 + 20 b - 12 = 0$

Hence, b is non-existent.

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The matrix 5103-2-46-1-2b is a singular matrix, if the value of b is (a) − 3 (b) 3 (c) 0 (d) non-existent

(d) non-existent For any singular matrix, the value of the determinant is 0. Here, A=5103-2-46-1-2bA=5(-4b+12)-10(-2b+6)+3(4-4)=0⇒-20b+60+20b-12=0 Hence, b is non-existent.

The matrix $[\begin{matrix} 5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b \end{matrix}]$ is a singular matrix, if the value of b is
(a) − 3
(b) 3
(c) 0
(d) non-existent

(d) non-existent
For any singular matrix, the value of the determinant is 0.
Here,

$A = [\begin{matrix} 5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b \end{matrix}] |A| = 5 (- 4 b + 12) - 10 (- 2 b + 6) + 3 (4 - 4) = 0 \Rightarrow - 20 b + 60 + 20 b - 12 = 0$

Hence, b is non-existent.