Let A = 2 & -1 3 & 4 , = B = 5 & 2 7 & 4 , C = 2 & 5 3 & 8 ,find … - Vidyadip

Question

$\text{Let A} = \begin{pmatrix} 2 & -1 \\ 3 & 4 \\ \end{pmatrix}, = \text{B} = \begin{pmatrix} 5 & 2 \\ 7 & 4 \\ \end{pmatrix}, \text{C} = \begin{pmatrix} 2 & 5 \\ 3 & 8 \\ \end{pmatrix},$find a matrix D such that CD – AB = O.

✓

Answer

$\text{Let D} = \begin{bmatrix} \text{x} & \text{y} \\ \text{z} & \text{w}\\ \end{bmatrix}$
$\text{CD} = \text{AB} \Rightarrow\begin{bmatrix} \text{2x + 5z} & \text{2y + 5w} \\ \text{3x + 8z} & \text{3y + 8w}\\ \end{bmatrix} = \begin{bmatrix} 3 & 0 \\ 43 & 22\\ \end{bmatrix}$
$\text{2x + 5z = 3, 3x + 8z = 43; 2y + 5w = 0, 3y + 8w = 22.}$
$\text{Solving, we get x = –191, y = –110, z = 77, w = 44}$
$\therefore \text{D} = \begin{bmatrix} -191 & -110\\ 77 & 44\\ \end{bmatrix}$

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 "5 Marks Questions" 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

Solve the following systems of linear equations by cramer's rule:

$6x + y - 3z = 5,$

$x + 3y - 2z = 5,$

$2x + y + 4z = 8$

If $\text{A}=\begin{bmatrix}\cos2\theta&\sin2\theta\\-\sin2\theta&\cos2\theta\end{bmatrix},$ find $A^2$.

Evaluate the following integrals:
$\int\frac{1}{\sin\text{x}(3+2\cos\text{x})}\ \text{dx}$

Find $\frac{\text{dy}}{\text{dx}}$
$\text{y}=\text{x}^{\sin\text{x}}+\big(\sin\text{x}\big)^\text{x}$

Solve the following systems of linear equations by cramer's rule:

If $f(x) = x^3 + 4x^2 - x,$ find $f(A),$ where $\text{A}=\begin{bmatrix}0&1&2\\2&-3&0\\1&-1&0\end{bmatrix}$

Solve the following initial value problems:
$\frac{\text{dy}}{\text{dx}}+\text{y}\cot\text{x}=2\cos\text{x},\text{ y}\Big(\frac{\pi}{2}\Big)=0$

In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater then 4. Find the expected value of the amount he wins or loses.

Let $d_1, d_2, d_3$ be three mutually exclusive diseases. Let $S$ be the set of observable symptoms of these diseases. $A$ doctor has the following information from a random sample of $5000$ patients: 1800 had disease $d_1, 2100$ has disease $d _2$, and others had disease $d _3 .1500$ patients with disease $d _1, 1200$ patients with disease $d _2$, and 900 patients with disease $d _3$ showed the symptom. Which of the diseases is the patient most likely to have?

Evaluate the following definite integral as limit of sum:$\int_\limits{0}^{4}\text{(x}+\text{e}^{2\text{x}})\ \text{dx}$