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Provide solution for rd sharma maths class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 17

Answers (1)

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option (d) non-existent

Given: \begin{bmatrix} 5 &10 &3 \\ -2&-4 &6 \\ -1& -2 &b \end{bmatrix}  is a singular matrices

Hint: for any singular matrix, the value of the determinant is 0

Solution:

\begin{aligned} &A=\left[\begin{array}{ccc} 5 & 10 & 3 \\ -2 & -4 & 6 \\ -1 & -2 & b \end{array}\right] \\ &|A|=5(-4 b+12)-10(-2 b+6)+3(4-4) \\ &=-20 b+60+20 b-60 \\ &=0 \end{aligned}

Hence, b is non-exist

 

∴ option (d) is correct

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