Solve the system of linear equations using th | vedclass

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

Question

(A) The given system of equations can be written in the form $AX = B$,where$A = \begin{bmatrix} 5 & 2 \ 3 & 2 \end{bmatrix}$,$X = \begin{bmatrix} x \

Vedclass · Accepted Answer

$x = -1, y = 4$

Vedclass · Answer

(A) The given system of equations can be written in the form $AX = B$,where$A = \begin{bmatrix} 5 & 2 \ 3 & 2 \end{bmatrix}$,$X = \begin{bmatrix} x \ y \end{bmatrix}$,and $B = \begin{bmatrix} 3 \ 5 \end{bmatrix}$.First,we calculate the determinant of $A$:$|A| = (5 	imes 2) - (2 	imes 3) = 10 - 6 = 4$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.$A^{-1} = \frac{1}{|A|} 	ext{adj}(A) = \frac{1}{4} \begin{bmatrix} 2 & -2 \ -3 & 5 \end{bmatrix}$.Now,$X = A^{-1}B$:$X = \frac{1}{4} \begin{bmatrix} 2 & -2 \ -3 & 5 \end{bmatrix} \begin{bmatrix} 3 \ 5 \end{bmatrix}$$X = \frac{1}{4} \begin{bmatrix} (2 	imes 3) + (-2 	imes 5) \ (-3 	imes 3) + (5 	imes 5) \end{bmatrix}$$X = \frac{1}{4} \begin{bmatrix} 6 - 10 \ -9 + 25 \end{bmatrix} = \frac{1}{4} \begin{bmatrix} -4 \ 16 \end{bmatrix} = \begin{bmatrix} -1 \ 4 \end{bmatrix}$.Thus,$x = -1$ and $y = 4$.

Solve the system of linear equations using the matrix method:
$5x + 2y = 3$
$3x + 2y = 5$

Similar Questions

Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$,and a system of linear equations
$x+y+z=5$
$x+2y+3z=\mu$
$x+3y+\lambda z=1$
is constructed. If $p$ is the probability that the system has a unique solution and $q$ is the probability that the system has no solution,then:

If the system of linear equations given by $x+y+z=3$,$2x+2y-z=3$,and $x+y-z=1$ is consistent and if $(x_0, y_0, z_0)$ is a solution,then $2x_0+2y_0+z_0=$

The system of linear equations $x + y + z = 2$,$2x + y - z = 3$,and $3x + 2y + kz = 4$ has a unique solution if

The system of equations $\begin{cases} \lambda x+y+3 z=0 \\ 2 x+\mu y-z=0 \\ 5 x+7 y+z=0 \end{cases}$ has infinitely many solutions in $\mathbb{R}$. Then,

Consider the system of equations: $x + y - az = 1$; $2x + ay + z = 1$; $ax + y - z = 2$. Which of the following statements is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Solve the system of linear equations using the matrix method:$5x + 2y = 3$$3x + 2y = 5$