Download App

Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices3 Marks
Question
Find the matrix $X$ so that $X\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right]=\left[\begin{array}{ccc}-7 & -8 & -9 \\ 2 & 4 & 6\end{array}\right]$
✓

Answer

Let $X = \left[ {\begin{array}{*{20}{c}} a&b \\ c&d \end{array}} \right]$
$\therefore \;\left[ {\begin{array}{*{20}{c}} a&b \\ c&d \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1 \\ 4 \end{array}\;\;\begin{array}{*{20}{c}} 2 \\ 5 \end{array}\;\;\begin{array}{*{20}{c}} 3 \\ 6 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 7} \\ 2 \end{array}\;\;\begin{array}{*{20}{c}} { - 8} \\ 4 \end{array}\;\;\begin{array}{*{20}{c}} { - 9} \\ 6 \end{array}} \right]$
$\left[ {\begin{array}{*{20}{c}} {a + 4b} \\ {c + 4d} \end{array}\;\;\begin{array}{*{20}{c}} {2a + 5b} \\ {2c + 5d} \end{array}\;\;\begin{array}{*{20}{c}} {3a + 6b} \\ {3c + 6d} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 7} \\ 2 \end{array}\;\;\begin{array}{*{20}{c}} { - 8} \\ 4 \end{array}\;\;\begin{array}{*{20}{c}} { - 9} \\ 6 \end{array}} \right]$
On solving a + 4b = -7 and 2a + 5b = -8 & c + 4d = 2 and 2c + 5d = 4
we get a = 1, b = -2, c = 2, d = 0
$X = \left[ {\begin{array}{*{20}{c}} 1&{ - 2} \\ 2&0 \end{array}} \right]$

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 "3 Marks Question" from Matrices→Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the value of $\tan^{-1}\Big(\frac{\text{x}}{\text{y}}\Big)-\tan^{-1}\Big(\frac{\text{x-y}}{\text{x+y}}\Big)$
→
Integrate the rational function $\frac{{5x}}{{\left( {x + 1} \right)\left( {{x^2} - 4} \right)}}$
→
Find the mean and standard deviation of the following probability distributions:
$x_i$ $1$ $2$ $3$ $4$
$p_i$ $0.4$ $0.3$ $0.2$ $0.1$
→
Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}(\text{x}-\text{a}){\sin}\Big(\frac{1}{\text{x}-\text{a}}\Big) & \text{x} \neq \text{a}\\\ 0, & \text{ x} = \text{a}\end{cases}\text{at x}=\text{a}$
→
Show that the following systems of linear equations has infinite number of solutions and solve:
x - y + 3z = 6,
x + 3y - 3z = -4,
5x + 3y + 3z = 10
→
The items produced by a company contain 10% defective items. Show that the probability of getting 2 defective items in a sample of 8 items is $\frac{28\times9^6}{10^8}$.
→
Solve system of linear equations, using matrix method.
x - y + 2z=7
3x + 4y - 5z = -5
2x - y + 3z = 12
→
Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_0\text{e}^{\text{x}}(\sin\text{x}-\cos\text{x})\text{dx}$
→
Prove the following:$\tan^{-1}\text{x}+\tan^{-1}\Bigg(\frac{\text{2x}}{\text{1 - x}^{2}}\Bigg)=\tan^{-1}\Bigg(\frac{\text{3x - x}^{2}}{\text{1 - 3x}^{2}}\Bigg)$.
→
Solve the following differential equations:$2\text{x}\frac{\text{dy}}{\text{dx}}=3\text{y},\text{y}(1)=2$
→