Linear Algebra

Determine the inverse of the matrix:

Hence, use the inverse to solve the simultaneous equations:

2 x+3 y-2 z=43 x

+5 y-4 z=10

x+2 y-3 z=9

Use Gaussian Elimination to solve:

x_{1}-2 x_{2}-x_{3}+3 x_{4}=4

2 x_{1}+x_{2}+x_{3}-4 x_{4}=3

3 x_{1}-x_{2}-2 x_{3}+2 x_{4}=6

x_{1}+3 x_{2}-x_{3}+x_{4}=8

Determine the four fourth roots of the complex number Z = 3 – 4j , using DeMoivre's theorem and express their values in cartesian form.



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