Question 12 Marks
If $A=\left|\begin{array}{ll}1 & 3 \\ 3 & 2\end{array}\right|$ and $B=\left|\begin{array}{ll}-2 & 3 \\ -4 & 1\end{array}\right|$ find $B A$
Answer$BA =\left|\begin{array}{ll}-2 & 3 \\ -4 & 1\end{array}\right|\left|\begin{array}{ll}1 & 3 \\ 3 & 2\end{array}\right| $
$ =\left|\begin{array}{cc}-2+9 & -6+6 \\ -4+3 & -12+2\end{array}\right| $
$=\left|\begin{array}{cc}7 & 0 \\ -1 & -10\end{array}\right|_{2 \times 2}$
View full question & answer→Question 22 Marks
If $A=\left|\begin{array}{ll}1 & 3 \\ 3 & 2\end{array}\right|$ and $B=\left|\begin{array}{ll}-2 & 3 \\ -4 & 1\end{array}\right|$ find $A B$
Answer$\begin{array}{l}A=\left|\begin{array}{ll}1 & 3 \\ 3 & 2\end{array}\right|_{2 \times 2} B=\left|\begin{array}{ll}-2 & 3 \\ -4 & 1\end{array}\right|_{2 \times 2} \end{array} $
$ \left.A B=\left|\begin{array}{cc}1 & 3 \\ 3 & 2\end{array}\right| \begin{array}{cc}-2 & 3 \\ -4 & 1\end{array} \right\rvert\, $
$ =\left|\begin{array}{cc}-2-12 & 3+3 \\ -6-8 & 9+2\end{array}\right|$
$=\left|\begin{array}{cc}-14 & 6 \\ -14 & 11\end{array}\right|_{2 \times 2}$
View full question & answer→Question 32 Marks
Evaluate the following:
$
\left|\begin{array}{ccc}
0 & 1 & 0 \\
2 & 0 & -3 \\
1 & 0 & -2
\end{array}\right|\left|\begin{array}{cc}
1 & -2 \\
3 & 4 \\
0 & 0
\end{array}\right|
$
Answer$\left|\begin{array}{ccc}0 & 1 & 0 \\ 2 & 0 & -3 \\ 1 & 0 & -2\end{array}\right|_{3 \times 3}\left|\begin{array}{cc}1 & -2 \\ 3 & 4 \\ 0 & 0\end{array}\right|_{3 \times 2}$
$=\left|\begin{array}{cc}0+3+0 & 0+4+0 \\ 2+0+0 & -4+0+0 \\ 1+0+0 & -2+0+0\end{array}\right|$
$=\left|\begin{array}{cc}3 & 4 \\ 2 & -4 \\ 1 & -2\end{array}\right|_{3 \times 2}$
View full question & answer→Question 42 Marks
Evaluate the following:
$
\left|\begin{array}{ll}
6 & 1 \\
3 & 1 \\
2 & 4
\end{array}\right|\left|\begin{array}{ccc}
1 & -2 & 1 \\
2 & 1 & 3
\end{array}\right|
$
Answer$\left|\begin{array}{ll}6 & 1 \\ 3 & 1 \\ 2 & 4\end{array}\right|_{3 \times 2}\left|\begin{array}{ccc}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right|_{2 \times 3}$
$=\left|\begin{array}{ccc}6+2 & -12+1 & 6+3 \\ 3+2 & -6+1 & 3+3 \\ 2+8 & -4+4 & 2+12\end{array}\right|$
$=\left|\begin{array}{ccc}8 & -11 & 9 \\ 5 & -5 & 6 \\ 10 & 0 & 14\end{array}\right|_{3 \times 3}$
View full question & answer→Question 52 Marks
Evaluate the following $: \left|\begin{array}{cc} 0 & 1 \\ -1 & 2 \\ -2 & 0 \end{array}\right|\left|\begin{array}{ccc} 0 & -4 & 0 \\ 3 & 0 & -1 \end{array}\right| $
Answer$\begin{array}{l}\left|\begin{array}{cc}0 & 1 \\ -1 & 2 \\ -2 & 0\end{array}\right|_{3 \times 2}\left|\begin{array}{ccc}0 & -4 & 0 \\ 3 & 0 & -1\end{array}\right|_{2 \times 3} \end{array} $
$ =\left|\begin{array}{ccc}0+3 & 0+0 & 0-1 \\ 0+6 & 4+0 & 0-2 \\ 0+0 & 8+0 & 0+0\end{array}\right| $
$ =\left|\begin{array}{ccc}3 & 0 & -1 \\ 6 & 4 & -2 \\ 0 & 8 & 0\end{array}\right|_{3 \times 3}$
View full question & answer→Question 62 Marks
Evaluate the following $: \left|\begin{array}{ll} 2 & 1 \\ 3 & 2 \\ 1 & 1 \end{array}\right|\left|\begin{array}{ccc} 1 & -2 & 1 \\ 2 & 1 & 3 \end{array}\right| $
Answer$\begin{array}{l}\left|\begin{array}{cc}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right|_{3 \times 2}\left|\begin{array}{ccc}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right|_{2 \times 3} \end{array} $
$ =\left|\begin{array}{ccc}2+2 & -4+1 & 2+3 \\ 3+4 & -6+2 & 3+6 \\ 1+2 & -2+1 & 1+3\end{array}\right| $
$ =\left|\begin{array}{ccc}4 & -3 & 5 \\ 7 & -4 & 9 \\ 3 & -1 & 4\end{array}\right|_{3 \times 3}$
View full question & answer→Question 72 Marks
Evaluate the following $ :\left|\begin{array}{cc} 2 & 3 \\ -4 & 0 \end{array}\right|\left|\begin{array}{cc} 3 & -2 \\ -1 & 4 \end{array}\right| $
Answer$\begin{array}{l}\left|\begin{array}{cc}2 & 3 \\ -4 & 0\end{array}\right|_{2 \times 2}\left|\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right|_{2 \times 2} \end{array} $
$ =\left|\begin{array}{cc}6-3 & -4+12 \\ -12+0 & 8+0\end{array}\right| $
$ =\left|\begin{array}{cr}3 & 8 \\ -12 & 8\end{array}\right|_{2 \times 2}$
View full question & answer→Question 82 Marks
Evaluate the following $: \left|\begin{array}{ll} 1 & 1 \\ 2 & 3 \end{array}\right|\left|\begin{array}{ll} 2 & 1 \\ 1 & 4 \end{array}\right| $
Answer$\begin{array}{l}\left|\begin{array}{ll}1 & 1 \\ 2 & 3\end{array}\right|_{2 \times 2}\left|\begin{array}{cc}2 & 1 \\ 1 & 4\end{array}\right|_{2 \times 2} \end{array} $
$=\left|\begin{array}{cc}2+1 & 1+4 \\ 4+3 & 2+12\end{array}\right| $
$=\left|\begin{array}{cc}3 & 5 \\ 7 & 14\end{array}\right|_{2 \times 2}$
View full question & answer→Question 92 Marks
Evaluate the following $: \left|\begin{array}{cc} 2 & -5 \\ 0 & -3 \end{array}\right|\left|\begin{array}{cc} 1 & -1 \\ 3 & 2 \end{array}\right| $
Answer$\begin{array}{l}\left|\begin{array}{cc}2 & -5 \\ 0 & -3\end{array}\right|_{2 \times 2}\left|\begin{array}{cc}1 & -1 \\ 3 & 2\end{array}\right|_{2 \times 2} \end{array} $
$ =\left|\begin{array}{cc}2-15 & -2-10 \\ 0-9 & 0-6\end{array}\right|_2 $
$ =\left|\begin{array}{cc}-13 & -12 \\ -9 & -6\end{array}\right|_{2 \times 2}$
View full question & answer→Question 102 Marks
Evaluate the following $ :\left|\begin{array}{cc} -2 & 3 \\ -1 & 4 \end{array}\right|\left|\begin{array}{cc} 6 & 4 \\ 3 & -1 \end{array}\right| $
Answer$\begin{array}{l}\left|\begin{array}{cc}-2 & 3 \\ -1 & 4\end{array}\right|_{2 \times 2}\left|\begin{array}{cc}6 & 4 \\ 3 & -1\end{array}\right|_{2 \times 2} \end{array} $
$ =\left|\begin{array}{cc}-2 \times 6+3 \times 3 & -8-3 \\ -6+4 \times 3 & -4-4\end{array}\right| $
$ =\left|\begin{array}{cc}-3 & -11 \\ 6 & -8\end{array}\right|_{2 \times 2}$
View full question & answer→Question 112 Marks
If $M =\left|\begin{array}{ll}8 & 3 \\ 9 & 7 \\ 4 & 3\end{array}\right|$ and $N =\left|\begin{array}{cc}4 & 7 \\ 5 & 3 \\ 10 & 1\end{array}\right|$ find $M - N$
Answer$\begin{array}{l}M=\left|\begin{array}{ll}8 & 3 \\ 9 & 7 \\ 4 & 3\end{array}\right|_{3 \times 2} \quad N=\left|\begin{array}{cc}4 & 7 \\ 5 & 3 \\ 10 & 1\end{array}\right|_{3 \times 2} \end{array} $
$M-N=\left|\begin{array}{cc}8-4 & 3-7 \\ 9-5 & 7-3 \\ 4+10 & 3+1\end{array}\right|$
$=\left|\begin{array}{cc}4 & -4 \\ 4 & 4 \\ -6 & 2\end{array}\right|$
View full question & answer→Question 122 Marks
If $M =\left|\begin{array}{ll}8 & 3 \\ 9 & 7 \\ 4 & 3\end{array}\right|$ and $N =\left|\begin{array}{cc}4 & 7 \\ 5 & 3 \\ 10 & 1\end{array}\right|$ find $M + N$
Answer$\begin{array}{l}M=\left|\begin{array}{ll}8 & 3 \\ 9 & 7 \\ 4 & 3\end{array}\right|_{3 \times 2}, N =\left|\begin{array}{cc}4 & 7 \\ 5 & 3 \\ 10 & 1\end{array}\right|_{3 \times 2} \end{array} $
$ M + N =\left|\begin{array}{cc}8+4 & 3+7 \\ 9+5 & 7+3 \\ 4+10 & 3+1\end{array}\right|$
$=\left|\begin{array}{cc}12 & 10 \\ 14 & 10 \\ 14 & 4\end{array}\right|_{3 \times 2}$
View full question & answer→Question 132 Marks
If $A=\left|\begin{array}{lll}17 & 5 & 19 \\ 11 & 8 & 13\end{array}\right|$ and $B=\left|\begin{array}{lll}9 & 3 & 7 \\ 1 & 6 & 5\end{array}\right|$, find $2 A-3 B$
Answer$\begin{array}{l}A=\left|\begin{array}{ccc}17 & 5 & 19 \\ 11 & 8 & 13\end{array}\right|_{2 \times 3} B=\left|\begin{array}{ccc}9 & 3 & 7 \\ 1 & 6 & 5\end{array}\right|_{2 \times 3} \end{array} $
$ 2 A-3 B=\left|\begin{array}{lll}34 & 10 & 38 \\ 22 & 16 & 26\end{array}\right|-\left|\begin{array}{ccc}27 & 9 & 21 \\ 3 & 18 & 15\end{array}\right| $
$ =\left|\begin{array}{ccc}7 & 1 & 17 \\ 19 & -2 & 11\end{array}\right|_{2 \times 3}$
View full question & answer→Question 142 Marks
If $P =\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right|$ and $Q =\left|\begin{array}{ll}7 & 3 \\ 4 & 1\end{array}\right|$ find $3 P - 2Q$
Answer$\begin{array}{l}=\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right|_{2 \times 2}, Q=\left|\begin{array}{ll}7 & 3 \\ 4 & 1\end{array}\right|_{2 \times 2}\end{array} $
$3 P-2 Q=\left|\begin{array}{cc}6 & 27 \\ 15 & 21\end{array}\right|-\left|\begin{array}{cc}14 & 6 \\ 8 & 2\end{array}\right| $
$ =\left|\begin{array}{cc}6-14 & 27-6 \\ 15-8 & 21-2\end{array}\right|$
$=\left|\begin{array}{cc}-8 & 21 \\ 7 & 19\end{array}\right|_{2 \times 2}$
View full question & answer→Question 152 Marks
If $P=\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right|$ and $Q=\left|\begin{array}{ll}7 & 3 \\ 4 & 1\end{array}\right|$ find $2Q - P$
Answer$\begin{array}{l}=\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right|_{2 \times 2}, Q=\left|\begin{array}{ll}7 & 3 \\ 4 & 1\end{array}\right|_{2 \times 2} \end{array} $
$ 2 Q-P=\left|\begin{array}{cc}14 & 6 \\ 8 & 2\end{array}\right|-\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right| $
$ =\left|\begin{array}{cc}14-2 & 6-9 \\ 8-5 & 2-7\end{array}\right|$
$=\left|\begin{array}{c}12-3 \\ 3-5\end{array}\right|_{2 \times 2}$
View full question & answer→Question 162 Marks
If $P=\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right|$ and $Q=\left|\begin{array}{ll}7 & 3 \\ 4 & 1\end{array}\right|$, find $2 P+3 Q$
Answer$\begin{array}{l}=\left|\begin{array}{ll}2 & 9 \\ 5 & 7\end{array}\right|_{2 \times 2}, Q=\left|\begin{array}{ll}7 & 3 \\ 4 & 1\end{array}\right|_{2 \times 2}\end{array} $
$ 2 P+3 Q=\left|\begin{array}{cc}4 & 18 \\ 10 & 14\end{array}\right|+\left|\begin{array}{cc}21 & 9 \\ 12 & 3\end{array}\right| $
$ =\left|\begin{array}{cc}4+21 & 18+9 \\ 10+12 & 14+3\end{array}\right|$
$=\left|\begin{array}{cc}25 & 27 \\ 22 & 17\end{array}\right|_{2 \times 2}$
View full question & answer→Question 172 Marks
If $A = [4 7]$ and $B = [3 l],$ find : $2A - 3B$
Answer$A =\left[4,7\right]_{1 \times 2} B $
$=\left[3 1\right]_{1 \times 2}$
$2 A -3 B =\left[8 14\right]-\left[9 3\right]$
$=|-1 11|_{1 \times 2}$
View full question & answer→Question 182 Marks
If $A = [4 7]$ and $B = [3 l],$ find: $A - B$
Answer$ A =\left[4 7\right]_{1 \times 2} B =\left[3 1\right]_{1 \times 2}$
$A - B =\left[4-3 7-1\right]$
$=\left|1 6\right|_{1 \times 2}$
View full question & answer→Question 192 Marks
If $A = [4 7]$ and $B = [3 1] ,$ find: $A+2B$
Answer$ A =\left[4 7\right]_{1 \times 2} B =\left[3 1\right]_{1 \times 2}$
$A+2 B=[4,7]+[6,2]$
$=\left[4+6 7+2\right]$
$=\left[10 9\right]_{1 \times 2}$
View full question & answer→Question 202 Marks
If $A =\left|\begin{array}{l}1215 \\ 1117\end{array}\right|$ and $B =\left|\begin{array}{ll}2 & 7 \\ 4 & 9\end{array}\right|$ find $A -2 B$
Answer$\begin{array}{l}A=\left|\begin{array}{ll}12 & 15 \\ 11 & 17\end{array}\right|_{2 \times 2}, B=\left|\begin{array}{ll}2 & 7 \\ 4 & 9\end{array}\right|_{2 \times 2} \end{array} $
$ 2 B=\left|\begin{array}{lll}4 & 1 & 4 \\ 8 & 1 & 8\end{array}\right| $
$ A-2 B=\left|\begin{array}{cc}12-4 & 15-14 \\ 11-8 & 17-18\end{array}\right| $
$ =\left|\begin{array}{cc}8 & 1 \\ 3 & -1\end{array}\right|_{2 \times 2}$
View full question & answer→Question 212 Marks
If $A=\left|\begin{array}{l}1215 \\ 1117\end{array}\right|$ and $B=\left|\begin{array}{ll}2 & 7 \\ 4 & 9\end{array}\right|$, find $:A+B$
Answer$\begin{array}{l}A=\left|\begin{array}{ll}12 & 15 \\ 11 & 17\end{array}\right|_{2 \times 2}, B=\left|\begin{array}{ll}2 & 7 \\ 4 & 9\end{array}\right|_{2 \times 2} \end{array} $
$ A+B=\left|\begin{array}{ll}12+2 & 15+7 \\ 11+4 & 17+9\end{array}\right| $
$ =\left|\begin{array}{ll}14 & 22 \\ 15 & 26\end{array}\right|_{2 \times 2}$
View full question & answer→Question 222 Marks
If $B=\left|\begin{array}{ll}15 & 13 \\ 11 & 12 \\ 10 & 17\end{array}\right|$, find the transpose of matrix Band If possible find the sum of the two matrices. If not possible state the reason.
Answer$\begin{aligned} B & =\left|\begin{array}{ll}15 & 13 \\ 11 & 12 \\ 10 & 17\end{array}\right|_{3 \times 2} \\ B ^{ t } & =\left|\begin{array}{lll}15 & 11 & 10 \\ 13 & 12 & 17\end{array}\right|_{2 \times 3}\end{aligned}$
To add two ma01xes their order 1.e. their corresponding number of rows and number of columns should be same, whereas in this case order of Band B' are not same hence, we cannot add them.
View full question & answer→Question 232 Marks
If $P =\left|\begin{array}{ll}8 & 5 \\ 7 & 2\end{array}\right|$ find $P - Pt$
Answer$\begin{array}{l}P=\left|\begin{array}{ll}8 & 5 \\ 7 & 2\end{array}\right|_{2 \times 2} \end{array} $
$ P-P^t=\left|\begin{array}{ll}8 & 5 \\ 7 & 2\end{array}\right|-\left|\begin{array}{ll}8 & 7 \\ 5 & 2\end{array}\right| $
$ =\left|\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right|_{2 \times 2}$
View full question & answer→Question 242 Marks
If $P= (8,5),(7,2)$ find $:P + P^t$
Answer$\begin{array}{l}P=\left|\begin{array}{ll}8 & 5 \\ 7 & 2\end{array}\right|_{2 \times 2} \end{array} $
$ P+P^t=\left|\begin{array}{ll}8 & 5 \\ 7 & 2\end{array}\right|+\left|\begin{array}{ll}8 & 7 \\ 5 & 2\end{array}\right| $
$ =\left|\begin{array}{cc}16 & 12 \\ 12 & 4\end{array}\right|_{2 \times 2}$
View full question & answer→