MCQ_SINGLE

If \(\begin{bmatrix}x&2&0\end{bmatrix}\begin{bmatrix}5\\ -1\\ x\end{bmatrix}=\begin{bmatrix}3&1\end{bmatrix}\begin{bmatrix}-2\\ x\end{bmatrix},\) then value of x is:

LA

If A is a $3\times3$ invertible matrix, show that for any scalar $k\ne0$, $(kA)^{-1}=\frac{1}{k}A^{-1}$. Hence calculate $(3A)^{-1}$, where $A=\begin{bmatrix}2&-1&1\\ -1&2&-1\\ 1&-1&2\end{bmatrix}$.

MCQ_SINGLE

If |A|=2, where A is a $2\times2$ matrix, then |4$A^{-1}$| equals :

MCQ_SINGLE

A matrix B = $[b_{ij}]_{m \times m}$ is said to be a diagonal matrix, if :

MCQ_SINGLE

If A is a square matrix of order 3 such that the value of \(|adj\cdot A|=8,\) then the value of \(|A^{T}|\) is:

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