Left[ {begin{array}{*{20}{c}}7&1&29&2&1end{array}} right],left[ begin{array}{l}345en

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3 and 4 .Determinants and Matrices

easy

$\left[ {\begin{array}{*{20}{c}}7&1&2\\9&2&1\end{array}} \right]\,\left[ \begin{array}{l}3\\4\\5\end{array} \right] + 2\left[ \begin{array}{l}4\\2\end{array} \right]$ is equal to

$\left[ \begin{array}{l}43\\44\end{array} \right]$

$\left[ \begin{array}{l}43\\45\end{array} \right]$

$\left[ \begin{array}{l}45\\44\end{array} \right]$

$\left[ \begin{array}{l}44\\45\end{array} \right]$

Solution

(a) $\left[ {\begin{array}{*{20}{c}}7&1&2\\9&2&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}3\\4\\5\end{array}} \right]\, = \,\,\left[ {\begin{array}{*{20}{c}}{35}\\{40}\end{array}} \right]$;

$\therefore$ $\left[ {\begin{array}{*{20}{c}}{35}\\{40}\end{array}} \right]\, + \,\left[ {\begin{array}{*{20}{c}}8\\4\end{array}} \right]\, = \,\left[ {\begin{array}{*{20}{c}}{43}\\{44}\end{array}} \right]$.

Standard 12

Mathematics

Which is true about matrix multiplication

normal

Find the value of $x, \,y$ and $z$ from the following equation : $\left[\begin{array}{ll}4 & 3 \\ x & 5\end{array}\right]=\left[\begin{array}{ll}y & z \\ 1 & 5\end{array}\right]$

easy

If $\omega \ne 1$ is cube root of unity and $H = \left[ {\begin{array}{*{20}{c}}\omega &0\\0&\omega \end{array}} \right]$ then ${H^{70}}$ is equal to

medium

(AIEEE-2011)

If $A=\left[\begin{array}{rrr}1 & 2 & 3 \\ 3 & -2 & 1 \\ 4 & 2 & 1\end{array}\right],$ then show that $A^{3}-23 A-40I=0$

medium

Suppose $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ is a real matrix with non-zero entries, $\alpha d-b c=0$ and $A^2=A$. Then, $a + d$ equals

hard

(KVPY-2018)