If $A^{\prime}=\begin{bmatrix}-2 & 3 \\ 1 & 2\end{bmatrix}$ and $B=\begin{bmatrix}-1 & 0 \\ 1 & 2\end{bmatrix},$ then find $(A+2B)^{\prime}$.
- A$\begin{bmatrix}-4 & 5 \\ 1 & 6\end{bmatrix}$
- B$\begin{bmatrix}-4 & 1 \\ 5 & 6\end{bmatrix}$
- C$\begin{bmatrix}-4 & 3 \\ 2 & 6\end{bmatrix}$
- D$\begin{bmatrix}-4 & 2 \\ 3 & 6\end{bmatrix}$
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Consider the following information regarding the number of men and women workers in three factories $I, II$ and $III$.
Factory Men and Women Workers $I$ $30$ Men,$25$ Women $II$ $25$ Men,$31$ Women $III$ $27$ Men,$26$ Women
Represent the above information in the form of a $3 \times 2$ matrix. What does the entry in the third row and second column represent?
| Factory | Men and Women Workers |
|---|---|
| $I$ | $30$ Men,$25$ Women |
| $II$ | $25$ Men,$31$ Women |
| $III$ | $27$ Men,$26$ Women |
Represent the above information in the form of a $3 \times 2$ matrix. What does the entry in the third row and second column represent?
Easy
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If $A = \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}$,then $A^n = \begin{bmatrix} 1 & 0 \\ n & 1 \end{bmatrix}$ for all $n \in N$. Which of the following is correct?
If $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$,then $A^{100} = $ . . . . . . .
The order of $[x\,y\,z]\,\,\left[ {\begin{array}{*{20}{c}}a&h&g\\h&b&f\\g&f&c\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right]$ is
Easy
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