Name: Classification and Operations of Matrices
Uploaded: 2019-07-19
Duration: 7 min 8 s
Description: There are various types of matrices formed based on the rows, columns and elements, watch this video to know about the types and different operations on matrices.

Question

Find $X$ and $Y$ , if $X + Y = [\begin{array}{l} 7 & 0 \\ 2 & 5 \end{array}]$ and $X - Y = [\begin{array}{l} 3 & 0 \\ 0 & 3 \end{array}]$

Accepted Answer

Given:
$Y$ and

$X - Y = [\begin{array}{l} 3 & 0 \\ 0 & 3 \end{array}] \dots \dots (2)$

Adding equation $(1)$ and $(2)$ , we get

$X + Y + X - Y = [\begin{array}{l} 7 & 0 \\ 2 & 5 \end{array}] + [\begin{array}{l} 3 & 0 \\ 0 & 3 \end{array}]$

$\Rightarrow 2 X = [\begin{array}{l} 7 + 3 & 0 + 0 \\ 2 + 0 & 5 + 3 \end{array}]$

$2 X = [\begin{array}{l} 10 & 0 \\ 2 & 8 \end{array}]$

$\Rightarrow X = \frac{1}{2} [\begin{array}{l} 10 & 0 \\ 2 & 8 \end{array}]$

$\Rightarrow X = [\begin{array}{l} \frac{10}{2} & \frac{0}{2} \\ \frac{2}{2} & \frac{8}{2} \end{array}]$

$\Rightarrow X = [\begin{array}{l} 5 & 0 \\ 1 & 4 \end{array}]$

Putting the value of $X$ in equation $(1),$ we get

$[\begin{array}{l} 5 & 0 \\ 1 & 4 \end{array}] + Y = [\begin{array}{l} 7 & 0 \\ 2 & 5 \end{array}]$

$Y = [\begin{array}{l} 7 & 0 \\ 2 & 5 \end{array}] - [\begin{array}{l} 5 & 0 \\ 1 & 4 \end{array}]$

$\Rightarrow Y = [\begin{array}{l} 7 - 5 & 0 - 0 \\ 2 - 1 & 5 - 4 \end{array}]$

$\Rightarrow Y = [\begin{array}{l} 2 & 0 \\ 1 & 1 \end{array}]$

Therefore, $X = [\begin{array}{l} 5 & 0 \\ 1 & 4 \end{array}]$ and $Y = [\begin{array}{l} 2 & 0 \\ 1 & 1 \end{array}]$ .

Find $X$ and $Y$ , if $X + Y = [\begin{array}{l} 7 & 0 \\ 2 & 5 \end{array}]$ and $X - Y = [\begin{array}{l} 3 & 0 \\ 0 & 3 \end{array}]$

Important Questions on Matrices

Learn and Prepare for any exam you want !

Find X and Y, if X+Y=7025 and X-Y=3003

Important Questions on Matrices

Learn and Prepare for any exam you want !

Find $X$ and $Y$ , if $X + Y = [\begin{array}{l} 7 & 0 \\ 2 & 5 \end{array}]$ and $X - Y = [\begin{array}{l} 3 & 0 \\ 0 & 3 \end{array}]$