Examine the consistency of the system of equa | vedclass

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

Question

(A) The given system of equations is:$2x - y = 5$$x + y = 4$The system can be written in the matrix form $AX = B$,where:$A = \begin{bmatrix} 2 & -1 \

Vedclass · Accepted Answer

Consistent

Vedclass · Answer

(A) The given system of equations is:$2x - y = 5$$x + y = 4$The system can be written in the matrix form $AX = B$,where:$A = \begin{bmatrix} 2 & -1 \ 1 & 1 \end{bmatrix}$,$X = \begin{bmatrix} x \ y \end{bmatrix}$,and $B = \begin{bmatrix} 5 \ 4 \end{bmatrix}$.Now,calculate the determinant of matrix $A$:$|A| = (2)(1) - (-1)(1) = 2 + 1 = 3$.Since $|A| 
eq 0$,the matrix $A$ is non-singular and invertible.Therefore,the system of equations has a unique solution and is consistent.

Examine the consistency of the system of equations: $2x - y = 5$ and $x + y = 4$.

Similar Questions

If the system of linear equations $x_1 + 2x_2 + 3x_3 = 6$,$x_1 + 3x_2 + 5x_3 = 9$,and $2x_1 + 5x_2 + ax_3 = b$ is consistent and has an infinite number of solutions,then:

If the system of linear equations $2x + 3y - z = -2$; $x + y + z = 4$; $x - y + |\lambda|z = 4\lambda - 4$ (where $\lambda \in R$) has no solution,then:

If the system of linear equations $x + ay + z = 3$,$x + 2y + 2z = 6$,and $x + 5y + 3z = b$ has no solution,then:

The following system of linear equations $7x + 6y - 2z = 0$; $3x + 4y + 2z = 0$; $x - 2y - 6z = 0$ has:

$A, C$ are $3 \times 3$ matrices. $B, D$ are $3 \times 1$ matrices. If $AX=B$ has a unique solution and $CX=D$ has an infinite number of solutions, then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module