Find the value of x, y and z from the followi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given the matrix equation: $\begin{bmatrix} x+y & 2 \ 5+z & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \ 5 & 8 \end{bmatrix}$.Since the matrices a

Vedclass · Accepted Answer

$x=4, y=2, z=0$ or $x=2, y=4, z=0$

Vedclass · Answer

(D) Given the matrix equation: $\begin{bmatrix} x+y & 2 \ 5+z & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \ 5 & 8 \end{bmatrix}$.Since the matrices are equal,their corresponding elements must be equal.Comparing the elements,we get:$1) x+y = 6$$2) xy = 8$$3) 5+z = 5$From equation $(3)$,$z = 5-5 = 0$.Now,we have $x+y = 6$ and $xy = 8$. We can use the identity $(x-y)^2 = (x+y)^2 - 4xy$.$(x-y)^2 = (6)^2 - 4(8) = 36 - 32 = 4$.Taking the square root,$x-y = \pm 2$.Case $1$: If $x-y = 2$ and $x+y = 6$,adding the equations gives $2x = 8 \Rightarrow x = 4$. Substituting $x=4$ into $x+y=6$ gives $y = 2$.Case $2$: If $x-y = -2$ and $x+y = 6$,adding the equations gives $2x = 4 \Rightarrow x = 2$. Substituting $x=2$ into $x+y=6$ gives $y = 4$.Thus,the values are $(x=4, y=2, z=0)$ or $(x=2, y=4, z=0)$.

Find the value of $x, y$ and $z$ from the following equation: $\begin{bmatrix} x+y & 2 \\ 5+z & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix}$

Similar Questions

The matrix $A = \frac{1}{3}\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ -2 & 2 & -1 \end{bmatrix}$ is

The order of matrix $A$ is $m \times n$ and for matrix $B$,if $AB^{\prime}$ and $B^{\prime}A$ are defined,then the order of matrix $B$ is . . . . . . .

The number of square matrices of order $5$ with entries from the set $\{0, 1\}$,such that the sum of all the elements in each row is $1$ and the sum of all the elements in each column is also $1$,is

Let $A = \begin{bmatrix} 0 & 1 \\ 1 & k \end{bmatrix}$,$k \in R$ and $A^3 = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$. If $d = 228$,then $b + c =$

If $2X - \begin{bmatrix} 1 & 2 \\ 7 & 4 \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 0 & -2 \end{bmatrix}$,then $X$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module