a) solve the following system of linear equations. x 1 - 2x 2 + 3x 3 = -2 -x 1 +

ID: 2945044 • Letter: A

Question

a) solve the following system of linear equations.

x1 - 2x2 + 3x3 = -2

-x1 + x2 - 2x3 = 3

2x1 - x2 + 3x3 = -7

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b) determine the inverse of the following matrix given that it is invertible.

[ 3 1 0 ]

C = [ -1 2 2 ]

[ 5 0 -1 ]

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c) express the following equations in the form AX = B and solve them using inverse of matrix.

3x + 2y - z = 4

2x - y + 2z =10

x - 3y - 4z = 5

The reduced row echelon form of the augmented matrix is

which corresponds to the system

x1=-1 x3-4

x2=1 x3-1

x3=arbitrary

Row
Operation
1: 1 -2 3 -2 -1 1 -2 3 2 -1 3 -7 add 1 times the 1st row to the 2nd row 1 -2 3 -2 0 -1 1 1 2 -1 3 -7

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