If A= [ ll 1 & 1 1 & 2 ], B= [ ll 4 & 1 3 & 1 ] and C= [ ll 24 & … - Vidyadip

Question

If $A=\left[\begin{array}{ll}1 & 1 \\ 1 & 2\end{array}\right], B=\left[\begin{array}{ll}4 & 1 \\ 3 & 1\end{array}\right]$ and $C=\left[\begin{array}{ll}24 & 7 \\ 31 & 9\end{array}\right]$ then find matrix $X$ such that $A X B=C$

✓

Answer

$\text{AXB}=C \\ \therefore\left(\begin{array}{ll}1 & 1 \\ 1 & 2\end{array}\right)(\mathrm{XB})=\left[\begin{array}{ll}24 & 7 \\ 31 & 9\end{array}\right]$
First we perform the row transformations.
By $R_2-R_1$, we get,
$\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right](X B)=\left[\begin{array}{rr}24 & 7 \\ 7 & 2\end{array}\right]$
By $R_1-R_2$, we get,
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right](X B)=\left[\begin{array}{rr}17 & 5 \\ 7 & 2\end{array}\right]$
$\therefore X B=\left[\begin{array}{rr}17 & 5 \\ 7 & 2\end{array}\right] $
$ \therefore X\left[\begin{array}{ll}4 & 1 \\ 3 & 1\end{array}\right]=\left[\begin{array}{rr}17 & 5 \\ 7 & 2\end{array}\right]$
Now, we perform the column transformations.
By $C_1 \leftrightarrow C_3$, we get,
$X\left[\begin{array}{ll}1 & 4 \\ 1 & 3\end{array}\right]=\left[\begin{array}{rr}5 & 17 \\ 2 & 7\end{array}\right]$
By $C_2-4 C_1$, we get,
$X\left[\begin{array}{rr}1 & 0 \\ 1 & -1\end{array}\right]=\left[\begin{array}{ll}5 & -3 \\ 2 & -1\end{array}\right]$
By $(-1) C_2$, we get,
$X\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]=\left[\begin{array}{ll}5 & 3 \\ 2 & 1\end{array}\right]$
By $C_1-C_2$, we get,
$X\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}2 & 3 \\ 1 & 1\end{array}\right]$
$\therefore X=\left[\begin{array}{ll}2 & 3 \\ 1 & 1\end{array}\right]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(5 Marks)" from Matrics→Matrics — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If a, b, c are the langths of sides, BC, CA and AB of a triangle ABC, prove that $\overrightarrow{\text{BC}}+\overrightarrow{\text{CA}}+\overrightarrow{\text{AB}}=\vec{\text{0}}$ and deduce that $\frac{\text{a}}{\sin\text{A}}=\frac{\text{b}}{\sin\text{B}}=\frac{\text{c}}{\sin\text{C}}.$

Evaluvate the following intregals
$\int\frac{1}{4+3\tan\text{x}}\ \text{dx}$

Find the distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z.

Find the particular solution of the differential equation $(\text{x}-\text{y})\frac{\text{dy}}{\text{dx}}=\text{x +2y},$ given that when x = 1, y = 0.

Find the nth derivative of the following:
log(2x + 3)

verify that $\text{y}^2=4\text{a}(\text{x}+\text{a})$ is a solution of the differential equation $\Big\{1-\Big(\frac{\text{dy}}{\text{dx}}\Big)^2\Big\}=2\text{x}\frac{\text{dy}}{\text{dx}}.$

For the following pairs of matrices verify that $(AB)^{-1} = B^{-1} A^{-1}$:$\text{A}=\begin{bmatrix}3 & 2 \\7 & 5 \end{bmatrix}\text{ and B}=\begin{bmatrix}4 & 6 \\3 & 2 \end{bmatrix}$

Find the equation of the plane through the point $2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}$ and passing throught the line of intersection of the planes $\vec{\text{r}}\cdot(\hat{\text{i}}+3\hat{\text{j}}-\hat{\text{k}})=0$ and $\vec{\text{r}}\cdot(\hat{\text{j}}+2\hat{\text{k}})=0.$

If $\text{f}(\text{a}+\text{b}-\text{x})=\text{f(x)},$ then prove that $\int\limits^{\text{b}}_\text{a}\text{x}\text{f(x)}\text{dx}=\frac{\text{a}+\text{b}}{2}\int\limits^{\text{b}}_\text{a}\text{f(x)}\text{dx}$

One kind of cake requires $300\ gm$ of flour and $15\ gm$ of fat, another kind of cake requires $150\ gm$ of flour and $30\ gm$ of fat. Find the maximum number of cakes which can be made from $7.5\ kg$ of flour and $600\ gm$ of fat, assuming that there is no shortage of the other ingradients used in making the cake. Make it as an $LPP$ and solve it graphically.