Let . If and , then…

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

Let

A=\begin{bmatrix}x&3&2\\1&y&4\\2&2&z\end{bmatrix}

. If

xyz=2\lambda

and

8x+4y+3z=\lambda+28

, then

\operatorname{adj}(A)A

equals (a)

\begin{bmatrix}\lambda+1&0&0\\0&\lambda+1&0\\0&0&\lambda+1\end{bmatrix}

(b)

\begin{bmatrix}\lambda&0&0\\0&\lambda&0\\0&0&\lambda\end{bmatrix}

(c)

\begin{bmatrix}\lambda^2&0&0\\0&\lambda^2&0\\0&0&\lambda^2\end{bmatrix}

(d)

\begin{bmatrix}\lambda+2&0&0\\0&\lambda+2&0\\0&0&\lambda+2\end{bmatrix}