Download App

Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Find x, y, a and b if $\begin{bmatrix}3\text{x}+4\text{y}&2&\text{x}-2\text{y}\\\text{a}+\text{b}&2\text{a}-\text{b}&^-1\end{bmatrix}=\begin{bmatrix}2&2&4\\5&-5&-1\end{bmatrix}$
✓

Answer

Since the corresponding elements of two equal matrices are equal,
$\begin{bmatrix}3\text{x}+4\text{y}&2&\text{x}-2\text{y}\\\text{a}+\text{b}&2\text{a}-\text{b}&^-1\end{bmatrix}=\begin{bmatrix}2&2&4\\5&-5&-1\end{bmatrix}$
⇒ 3x + 4y = 2 ...(1)
⇒ x - 2y = 4
⇒ x = 4 + 2y ...(2)
Putting the value of x in eq. (1), we get
3(4 + 2y) + 4y = 2
⇒ 12 + 6y + 4y = 2
⇒ 12 + 10y = 2
⇒ 10y = 2 - 12
⇒ 10y = -10
$\Rightarrow\text{y}=\frac{-10}{10}=-1$
Putting the value of y in eq. (2), we get
x = 4 + 2(-1)
⇒ x = 4 - 2 = 2
a + b = 5
⇒ a = 5 - b ...(3)
⇒ 2a - b = -5 ...(4)
Putting the value of a in eq. (4), we get
2(5 - b) - b = -5
⇒ 10 - 2b - b = -5
⇒ 10 - 3b = -5
⇒ -3b = -15
$\Rightarrow\text{b}=\frac{-15}{-3}$
⇒ b = 5
Putting the value of b in eq. (3), we get
a = 5 - 5
⇒ a = 0
$\therefore$ x = 2, y = -1, a = 0 and b = 5

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.(2 Marks)" from Algebra of Matrices→Algebra of Matrices — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If matrix $\text{A}=\begin{bmatrix}2&-2\\-2&2 \end{bmatrix}$ and $A^2= pA$, then write the value of p.
→
Evaluate:
$\cot\Big(\sin^{-1}\frac{3}{4}+\sec^{-1}\frac{4}{3}\Big)$
→
State whether $\text{f}(\text{x})=\tan\text{x}-\text{x}$ is increasing or decreasing its domain.
→
Find the vector equation of the plane which is at a distance of 5 units from the origin and which is normal to the vector $2 \hat{i}+\hat{j}+2 \hat{k}$
→
Find the area of the region bounded by the curves $x^2=16 y, y=1, y=4$ and the Y-axis, lying in the first quadrant.
→
Find the adjoint of the following matrices:$\text{C}=\begin{bmatrix} \cos\alpha & \sin\alpha \\ \sin\alpha & \cos\alpha \end{bmatrix}$
Verify that (adjoint A) A = |A|I = A (adjoint A) for the above matrices.
→
Integrate the following functions w.r.t x:

$\frac{20+12 e^x}{3 e^x+4}$

→
The probability distribution of random variable X is given below:
$\text{X}$
$0$
$1$
$2$
$3$
$\text{P}(\text{X})$
$\text{k}$
$\frac{\text{k}}{2}$
$\frac{\text{k}}{4}$
$\frac{\text{k}}{8}$
Determine $\text{P}(\text{X}\leq2)$ and $\text{P}(\text{X}>2)$
→
Find the approximate values of:

$e ^{0.995}$, given that $e =2.7183$.

→
Find the equation of the line passing through the points (2, -1, 3) and parallel to the line $\vec{\text{r}}=\big(\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}\big)+\lambda\big(2\hat{\text{i}}+3\hat{\text{j}}-5\hat{\text{k}}\big).$
→