Multiple Choice

1. What is the order of the matrix $A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix}$?

   $3 \times 2$

   $2 \times 2$

   $2 \times 3$

   $3 \times 3$

2. For the matrix $B = \begin{pmatrix} 10 & 11 & 12 \\ 13 & 14 & 15 \\ 16 & 17 & 18 \end{pmatrix}$, what is the element $b_{23}$?

   $15$

   $17$

   $13$

   $11$

3. Given $M = \begin{pmatrix} 3x & 7 \\ 2 & y \end{pmatrix}$ and $N = \begin{pmatrix} 9 & 7 \\ 2 & -5 \end{pmatrix}$. If $M = N$, what are the values of $x$ and $y$?

   $x=9, y=2$

   $x=3, y=-5$

   $x=7, y=-5$

   $x=3, y=5$

4. Let $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix}$. Calculate $A+B$.

   $\begin{pmatrix} 6 & 8 \\ 10 & 12 \end{pmatrix}$

   $\begin{pmatrix} 5 & 12 \\ 21 & 32 \end{pmatrix}$

   $\begin{pmatrix} 4 & 4 \\ 4 & 4 \end{pmatrix}$

   $\begin{pmatrix} 6 & 7 \\ 10 & 11 \end{pmatrix}$

5. Given matrices $X = \begin{pmatrix} 10 & 8 \\ 5 & 3 \end{pmatrix}$ and $Y = \begin{pmatrix} 2 & 1 \\ 3 & 0 \end{pmatrix}$. Calculate $X-Y$.

   $\begin{pmatrix} 8 & 7 \\ 2 & 3 \end{pmatrix}$

   $\begin{pmatrix} 8 & 9 \\ 2 & 3 \end{pmatrix}$

   $\begin{pmatrix} 12 & 9 \\ 8 & 3 \end{pmatrix}$

   $\begin{pmatrix} 8 & 7 \\ 2 & 3 \end{pmatrix}$

6. If $P = \begin{pmatrix} 2 & 4 \\ 6 & 8 \end{pmatrix}$, what is the result of $3P$?

   $\begin{pmatrix} 6 & 4 \\ 6 & 8 \end{pmatrix}$

   $\begin{pmatrix} 6 & 12 \\ 18 & 24 \end{pmatrix}$

   $\begin{pmatrix} 6 & 12 \\ 6 & 8 \end{pmatrix}$

   $\begin{pmatrix} 6 & 12 \\ 18 & 8 \end{pmatrix}$

7. Let $C = \begin{pmatrix} 1 & 0 & -1 \\ 2 & 3 & 4 \end{pmatrix}$ and $D = \begin{pmatrix} 5 & 2 & 1 \\ -2 & 0 & 3 \end{pmatrix}$. Find $C+D$.

   $\begin{pmatrix} 6 & 2 & 2 \\ 0 & 3 & 7 \end{pmatrix}$

   $\begin{pmatrix} 6 & 2 & 0 \\ 0 & 3 & 7 \end{pmatrix}$

   $\begin{pmatrix} 6 & 2 & 0 \\ 4 & 3 & 7 \end{pmatrix}$

   $\begin{pmatrix} 6 & 2 & 0 \\ 0 & 3 & 1 \end{pmatrix}$

8. Given $R = \begin{pmatrix} 10 & 5 \\ 8 & 3 \\ 2 & 1 \end{pmatrix}$ and $S = \begin{pmatrix} 3 & 2 \\ 1 & 0 \\ 4 & -1 \end{pmatrix}$. Calculate $R-S$.

   $\begin{pmatrix} 7 & 3 \\ 7 & 3 \\ -2 & 2 \end{pmatrix}$

   $\begin{pmatrix} 7 & 3 \\ 7 & 3 \\ 6 & 0 \end{pmatrix}$

   $\begin{pmatrix} 7 & 3 \\ 7 & 3 \\ -2 & 0 \end{pmatrix}$

   $\begin{pmatrix} 7 & 3 \\ 9 & 3 \\ -2 & 2 \end{pmatrix}$

9. If $T = \begin{pmatrix} 3 \\ -2 \\ 6 \end{pmatrix}$, what is the result of $-2T$?

   $\begin{pmatrix} -6 \\ 4 \\ 6 \end{pmatrix}$

   $\begin{pmatrix} -6 \\ -4 \\ -12 \end{pmatrix}$

   $\begin{pmatrix} -6 \\ 4 \\ -12 \end{pmatrix}$

   $\begin{pmatrix} 6 \\ -4 \\ 12 \end{pmatrix}$

10. A matrix that has only one row is called a:

    Square matrix

    Zero matrix

    Row matrix

    Column matrix

11. Given $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 5 & 6 & 7 \\ 8 & 9 & 10 \end{pmatrix}$. What is $A+B$?

    $\begin{pmatrix} 6 & 8 & 7 \\ 11 & 13 & 10 \end{pmatrix}$

    $\begin{pmatrix} 6 & 8 \\ 11 & 13 \end{pmatrix}$

    $\begin{pmatrix} 1 & 2 & 5 \\ 3 & 4 & 8 \end{pmatrix}$

    Undefined

12. Let $A = \begin{pmatrix} 1 & 0 \\ -1 & 2 \end{pmatrix}$ and $B = \begin{pmatrix} 3 & 1 \\ 0 & 4 \end{pmatrix}$. Find $2A+B$.

    $\begin{pmatrix} 4 & 1 \\ -1 & 6 \end{pmatrix}$

    $\begin{pmatrix} 5 & 1 \\ -2 & 4 \end{pmatrix}$

    $\begin{pmatrix} 5 & 1 \\ -2 & 8 \end{pmatrix}$

    $\begin{pmatrix} 5 & 0 \\ -2 & 8 \end{pmatrix}$

13. Given $A = \begin{pmatrix} 4 & 5 \\ 0 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 2 \\ -1 & 0 \end{pmatrix}$. Calculate $A-3B$.

    $\begin{pmatrix} 1 & -1 \\ -3 & 1 \end{pmatrix}$

    $\begin{pmatrix} 1 & -1 \\ -3 & 1 \end{pmatrix}$

    $\begin{pmatrix} 1 & 11 \\ 3 & 1 \end{pmatrix}$

    $\begin{pmatrix} 1 & -1 \\ 3 & 1 \end{pmatrix}$

14. Let $M = \begin{pmatrix} 2 & -1 \\ 0 & 3 \end{pmatrix}$ and $N = \begin{pmatrix} 1 & 1 \\ 2 & 0 \end{pmatrix}$. Find $2(M+N)$.

    $\begin{pmatrix} 6 & 0 \\ 4 & 6 \end{pmatrix}$

    $\begin{pmatrix} 6 & 0 \\ 2 & 6 \end{pmatrix}$

    $\begin{pmatrix} 4 & -2 \\ 0 & 6 \end{pmatrix}$

    $\begin{pmatrix} 4 & 0 \\ 4 & 6 \end{pmatrix}$

15. If $\begin{pmatrix} 4x & 8 \\ 1 & 2y \end{pmatrix} = \begin{pmatrix} 12 & 8 \\ 1 & -10 \end{pmatrix}$, what are the values of $x$ and $y$?

    $x=12, y=-10$

    $x=4, y=-10$

    $x=3, y=-5$

    $x=3, y=5$

16. Given $A = \begin{pmatrix} 1 & 2 \\ x & 4 \end{pmatrix}$, $B = \begin{pmatrix} 3 & -1 \\ 2 & 5 \end{pmatrix}$, and $A+B = \begin{pmatrix} 4 & 1 \\ 7 & 9 \end{pmatrix}$. What is the value of $x$?

    $x=5$

    $x=3$

    $x=1$

    $x=4$

17. If $4 \begin{pmatrix} 1 & 2 \\ 3 & y \end{pmatrix} = \begin{pmatrix} 4 & 8 \\ 12 & -20 \end{pmatrix}$, what is the value of $y$?

    $y=-4$

    $y=5$

    $y=-5$

    $y=4$

18. Let $A = \begin{pmatrix} 1 & 0 \\ 2 & 3 \end{pmatrix}$, $B = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$, and $C = \begin{pmatrix} 5 & -2 \\ 0 & 1 \end{pmatrix}$. Calculate $A+2B-C$.

    $\begin{pmatrix} -4 & -1 \\ 4 & 2 \end{pmatrix}$

    $\begin{pmatrix} 6 & -1 \\ 3 & 4 \end{pmatrix}$

    $\begin{pmatrix} -4 & 4 \\ 4 & 0 \end{pmatrix}$

    $\begin{pmatrix} -4 & 4 \\ 4 & 2 \end{pmatrix}$

19. What is a matrix where all its elements are zero called?

    Identity matrix

    Zero matrix

    Row matrix

    Square matrix

20. Given $M = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $N = \begin{pmatrix} 5 \\ 6 \end{pmatrix}$. What is $2M - N$?

    Undefined

    $\begin{pmatrix} 2 & 4 \\ 6 & 8 \end{pmatrix}$

    $\begin{pmatrix} -3 \\ 0 \end{pmatrix}$

    $\begin{pmatrix} -3 & 4 \\ -3 & 8 \end{pmatrix}$