Use back substitution to solve each of the following systems of equations: a) x_1-3x_2=2, 2x^2=6

VarceprewN3M

VarceprewN3M

Answered question

2022-11-28

Use back substitution to solve each of the following systems of equations:
a) x 1 3 x 2 = 2 2 x 2 = 6
b) x 1 + x 2 + x 3 = 8 2 x 2 + x 3 = 5 3 x 3 = 9
c) x 1 + 2 x 2 + 2 x 3 + x 4 = 5 3 x 2 + x 3 2 x 4 = 1 x 3 + 2 x 4 = 1 4 x 4 = 4
d) x 1 + x 2 + x 3 + x 4 + x 5 = 5 2 x 2 + x 3 2 x 4 + x 5 = 1 4 x 3 + x 4 2 x 5 = 1 x 4 3 x 5 = 0 2 x 5 = 2
Write out the coefficient matrix for each of the systems in first exercise.

Answer & Explanation

Aileen Powers

Aileen Powers

Beginner2022-11-29Added 12 answers

a )   x 1 3 x 2 = 2 2 x 1 = 6 x 2 = 3 x 1 9 = 2 x 1 = 11 b )   3 x 3 = 9 x 3 = 3 2 x 2 + x 3 = 5 2 x 2 = 2 x 1 = 1 x 1 + x 2 + x 3 = 8 x 1 4 c )   4 x 4 = 4 x 4 = 1 x 3 + 2 x 4 = 1 x 3 = 3 3 x 2 + x 3 2 x 4 = 1 x 2 = 0 x 1 + 2 x 2 + 2 x 3 + x 4 = 5 x 1 = 2 d )   2 x 5 = 2 x 5 = 1 x 4 3 x 5 = 0 x 4 = 3 4 x 3 + x 4 2 x 5 = 1 x 3 = 0 2 x 1 + x 3 2 x 4 + x 5 = 1 x 1 = 3 x 1 + x 2 + x 3 + x 4 + x 5 = 5 x 1 = 7
2) Coefficient matrix
a ) [ 1 3 0 2 ] b ) [ 1 1 1 0 2 1 0 0 3 ] c ) [ 1 2 2 1 0 3 1 2 0 0 1 2 0 0 0 4 ] d ) [ 1 1 1 1 1 0 2 1 2 1 0 0 4 1 2 0 0 0 1 3 0 0 0 0 2 ]

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