What are the values of (x, y, z, t) where 3{bmatrix} x & y \\ z & t {bmatrix} = {bmatrix} x & 6 \\ -1 & 2t {bmatrix} + {bmatrix} 4 & x+y \\ z+t & 3 {bmatrix}=?

Correct Answer is : (2,4,1,3)(2,4,1,3)(2,4,1,3)

Correct Answer is : (2,4,1,3)(2,4,1,3)(2,4,1,3)

Test Index

AP EAPCET 23-Aug-2021 Shift 2 Paper

Section: Mathematics

Question : 6 of 160

Marks: +1, -0

What are the values of

(x, y, z, t)

3\begin{bmatrix} x & y \\ z & t \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2t \end{bmatrix}

+ \begin{bmatrix} 4 & x+y \\ z+t & 3 \end{bmatrix}

Solution:

3\begin{bmatrix} x & y \\ z & t \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2t \end{bmatrix}

+ \begin{bmatrix} 4 & x+y \\ z+t & 3 \end{bmatrix}

\begin{bmatrix} 3x & 3y \\ 3z & 3t \end{bmatrix} = \begin{bmatrix} x+4 & 6+x+y \\ -1+z+t & 2t+3 \end{bmatrix}

On comparing two matrices are equal if their corresponding elements are equal

3x = x + 4 \Rightarrow x = 2

3t = 2t + 3 \Rightarrow t = 3

3z = -1 + z + t

\Rightarrow 3z = -1 + z + 3

\Rightarrow z = 1

3y = 6 + x + y

⇒

2y = 6 + 2 \Rightarrow y = 4

\therefore (x, y, z, t) = (2,4,1,3)

Go to Question:

Prev Question

Next Question