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Recent questions tagged matrix-algebra

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GATE Mechanical 2014 Set 4 | Question: 1
Which one of the following equations is a correct identity for arbitrary $3 \times 3$ real matrices $P$, $Q$ and $R$? $P(Q+R)=PQ+RP$ $(P-Q)^2 = P^2 -2PQ -Q^2$ $\text{det } (P+Q)= \text{det } P+ \text{det } Q$ $(P+Q)^2=P^2+PQ+QP+Q^2$
Which one of the following equations is a correct identity for arbitrary $3 \times 3$ real matrices $P$, $Q$ and $R$?$P(Q+R)=PQ+RP$$(P-Q)^2 = P^2 -2PQ -Q^2$$\text{det } ...
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GATE Mechanical 2014 Set 2 | Question: 18
If there are $m$ sources and $n$ destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is $m + n$ $m + n + 1$ $m + n − 1$ $m$
If there are $m$ sources and $n$ destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is$m + n$$m + n + 1$$m + n − ...
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GATE Mechanical 2014 Set 1 | Question: 4
The matrix form of the linear syatem $\dfrac{dx}{dt}=3x-5y$ and $\dfrac{dy}{dt}=4x+8y$ is $\dfrac{d}{dt}\begin{Bmatrix} x\\y \end{Bmatrix}=\begin{bmatrix} 3 & -5\\ 4& 8 \end{bmatrix}\begin{Bmatrix} x\\y \end{Bmatrix} \\$ ...
The matrix form of the linear syatem $\dfrac{dx}{dt}=3x-5y$ and $\dfrac{dy}{dt}=4x+8y$ is$\dfrac{d}{dt}\begin{Bmatrix} x\\y \end{Bmatrix}=\begin{bmatrix} 3 & -5\\ 4& 8 \e...
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