The number of solutions of the system of equa | vedclass

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

Question

(A) Given the system of equations: $2x + y - z = 7$ $(i)$ $x - 3y + 2z = 1$ $(ii)$ $x + 4y - 3z = 5$ $(iii)$ To check for consistency,we write the aug

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Given the system of equations: $2x + y - z = 7$ $(i)$ $x - 3y + 2z = 1$ $(ii)$ $x + 4y - 3z = 5$ $(iii)$ To check for consistency,we write the augmented matrix or use elimination. Multiply $(ii)$ by $2$: $2x - 6y + 4z = 2$ $(iv)$ Subtract $(iv)$ from $(i)$: $(2x + y - z) - (2x - 6y + 4z) = 7 - 2 \implies 7y - 5z = 5$ $(v)$ Now,subtract $(ii)$ from $(iii)$: $(x + 4y - 3z) - (x - 3y + 2z) = 5 - 1 \implies 7y - 5z = 4$ $(vi)$ Comparing $(v)$ and $(vi)$,we have $7y - 5z = 5$ and $7y - 5z = 4$. Since $5 
eq 4$,the system is inconsistent and has no solution. Therefore,the number of solutions is $0$.

The number of solutions of the system of equations $2x + y - z = 7$,$x - 3y + 2z = 1$,and $x + 4y - 3z = 5$ is

Similar Questions

The chlorination of ethane is an example of which of the following types of reactions?

The experimentally determined molar mass of a non-volatile solute,$BaCl_2$,in water by Cottrell's method,is

What is the composition of the white enamel of our teeth?

If $\hat{i}+2 \hat{j}+3 \hat{k}$ and $3 \hat{i}+2 \hat{j}+\hat{k}$ are sides of a parallelogram, then a unit vector parallel to one of the diagonals of the parallelogram is

$A$ car weighs $1800\,kg$. The distance between its front and back axles is $1.8\,m$. Its centre of gravity is $1.05\,m$ behind the front axle. Force exerted by the level ground on each front wheel is ........ $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module