Question
If $A=\left[\begin{array}{cc}2 & 1 \\ 0 & -2\end{array}\right]$ and $B=\left[\begin{array}{cc}4 & 1 \\ -3 & -2\end{array}\right], C=\left[\begin{array}{ll}-3 & 2 \\ -1 & 4\end{array}\right]$ Find $A^2+A C-5 B$
✓
Answer
$
\begin{aligned}
& A=\left[\begin{array}{cc}
2 & 1 \\
0 & -2
\end{array}\right] \\
& B=\left[\begin{array}{cc}
4 & 1 \\
-3 & -2
\end{array}\right] \\
& C=\left[\begin{array}{ll}
-3 & 2 \\
-1 & 4
\end{array}\right] \\
& A^2+A C-5 B \\
& =\left[\begin{array}{cc}
2 & 1 \\
0 & -2
\end{array}\right]\left[\begin{array}{cc}
2 & 1 \\
0 & -2
\end{array}\right]+\left[\begin{array}{cc}
2 & 1 \\
0 & -2
\end{array}\right]\left[\begin{array}{ll}
-3 & 2 \\
-1 & 4
\end{array}\right]-5\left[\begin{array}{cc}
4 & 1 \\
-3 & -2
\end{array}\right]
\end{aligned}
$
(Substituting the values from questions)
$
\begin{aligned}
& =\left[\begin{array}{ll}
4+0 & 2-2 \\
0+0 & 0+4
\end{array}\right]+\left[\begin{array}{cc}
-6-1 & 0+4 \\
0+2 & -8
\end{array}\right]-5\left[\begin{array}{cc}
4 & 1 \\
-3 & -2
\end{array}\right] \\
& =\left[\begin{array}{ll}
4 & 0 \\
0 & 4
\end{array}\right]+\left[\begin{array}{cc}
-7 & 8 \\
2 & -8
\end{array}\right]-\left[\begin{array}{cc}
20 & 5 \\
-15 & -10
\end{array}\right] \\
& =\left[\begin{array}{cc}
4-7-20 & 0+8-5 \\
0+2+15 & 4-8+10
\end{array}\right] \\
& =\left[\begin{array}{cc}
-23 & 3 \\
17 & 6
\end{array}\right] .
\end{aligned}
$
\begin{aligned}
& A=\left[\begin{array}{cc}
2 & 1 \\
0 & -2
\end{array}\right] \\
& B=\left[\begin{array}{cc}
4 & 1 \\
-3 & -2
\end{array}\right] \\
& C=\left[\begin{array}{ll}
-3 & 2 \\
-1 & 4
\end{array}\right] \\
& A^2+A C-5 B \\
& =\left[\begin{array}{cc}
2 & 1 \\
0 & -2
\end{array}\right]\left[\begin{array}{cc}
2 & 1 \\
0 & -2
\end{array}\right]+\left[\begin{array}{cc}
2 & 1 \\
0 & -2
\end{array}\right]\left[\begin{array}{ll}
-3 & 2 \\
-1 & 4
\end{array}\right]-5\left[\begin{array}{cc}
4 & 1 \\
-3 & -2
\end{array}\right]
\end{aligned}
$
(Substituting the values from questions)
$
\begin{aligned}
& =\left[\begin{array}{ll}
4+0 & 2-2 \\
0+0 & 0+4
\end{array}\right]+\left[\begin{array}{cc}
-6-1 & 0+4 \\
0+2 & -8
\end{array}\right]-5\left[\begin{array}{cc}
4 & 1 \\
-3 & -2
\end{array}\right] \\
& =\left[\begin{array}{ll}
4 & 0 \\
0 & 4
\end{array}\right]+\left[\begin{array}{cc}
-7 & 8 \\
2 & -8
\end{array}\right]-\left[\begin{array}{cc}
20 & 5 \\
-15 & -10
\end{array}\right] \\
& =\left[\begin{array}{cc}
4-7-20 & 0+8-5 \\
0+2+15 & 4-8+10
\end{array}\right] \\
& =\left[\begin{array}{cc}
-23 & 3 \\
17 & 6
\end{array}\right] .
\end{aligned}
$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A die is thrown once. Find the probability of getting a number: less than 3
Use a graph paper to answer the following questions. (Take 1 cm = 1 unit on both axis):
(i) Plot A (4, 4), B (4, – 6) and C (8, 0), the vertices of a triangle ABC.
(ii) Reflect ABC on the y-axis and name it as A’B’C’.
(iii) Write the coordinates of the images A’, B’ and C’.
(iv) Give a geometrical name for the figure AA’ C’B’ BC.
(v) Identify the line of symmetry of AA’ C’ B’ BC.
(i) Plot A (4, 4), B (4, – 6) and C (8, 0), the vertices of a triangle ABC.
(ii) Reflect ABC on the y-axis and name it as A’B’C’.
(iii) Write the coordinates of the images A’, B’ and C’.
(iv) Give a geometrical name for the figure AA’ C’B’ BC.
(v) Identify the line of symmetry of AA’ C’ B’ BC.
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and reactinto small cones of base radius 2 cm and height 8 cm. Find the number of cones.
If y is the mean proportional between x and z. prove that
$\frac{x^2-y^2+z^2}{x^{-2}-y^{-2}+z^{-2}}=y^4$
→$\frac{x^2-y^2+z^2}{x^{-2}-y^{-2}+z^{-2}}=y^4$
Solve the following inequalities and represent the solution set on a number line:
$3>\frac{2(3-4 x)}{7} \geq-2$.
→$3>\frac{2(3-4 x)}{7} \geq-2$.
Prove.
$\frac{\sin A}{1+\cos A}=\operatorname{cosec} A-\cot A$
→$\frac{\sin A}{1+\cos A}=\operatorname{cosec} A-\cot A$
The model of a building is constructed with scale factor $1: 30$.
(i) If the height of the model is 80 cm , find the actual height of the building in metre.
(ii) If the actual volume of the tank on the top of the building is $27 \mathrm{~m}^3$, find the volume of the tank on the top of the model.
→(i) If the height of the model is 80 cm , find the actual height of the building in metre.
(ii) If the actual volume of the tank on the top of the building is $27 \mathrm{~m}^3$, find the volume of the tank on the top of the model.
Draw histogram for the following distributions:
| Class Interval | 10-16 | 16-22 | 22-28 | 28-34 | 34-40 |
| Frequency | 15 | 23 | 30 | 20 | 16 |
In following figure , the incircle of Δ ABC , touches the sides BC , CA and AB at D , E and F respectively. Show AF + BD + CE = AE + BF + CD
For the G.P. $\frac{1}{27}, \frac{1}{9}, \frac{1}{3}, \ldots \ldots 81$
find the product of fourth term from the beginning and the fourth term from the end.
→find the product of fourth term from the beginning and the fourth term from the end.