Linear Algebra RGPV 2001

Question

Test the consistency of the following system of equations and solve if possible

$3x + 3y +2z = 1$

$x + 2y = 4$

$10y + 3z = -2$

$2x - 3y -z = 5$

Comments

answer consistent?

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unique solution :hence consistent.

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arvin and srestha what solutions you got? mine are not matching the answer

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i did it using augmented matrix form... and than using reduced row echelon method.. which gave rank(a) =rank(a|b)= 3(no. of variable) = so i found that its consistent and has unique solution..

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what is given ans?

Answer 1

"If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent ."

$3x+3y+2z=1$

$x+2y=4$

$10y+3z=-2$

$2x-3y-z=5$

We can write it as

$3x+3y+2z=1$

$x+12y+3z=2$

$2x-3y-z=5$

and solve them inividually

So, it will be consistent solution