Consider the following system of linear equations. x-3y=-5

y+3z=-1

2x-10y+2z=-20

i. Write the system in the form A . (1 mark)

ii. Find the inverse of A using the Gauss-Jordan elimination. (4 marks)

iii. Evaluate det(A) using co-factor method. (2 marks)

iv. Find the inverse of A using the determinant and the adjoint of A, i. e.,

A-¹ = -

(A)

Check that your answer coincides with your answer in part (ii). (4 marks)

v. Find the

-factorization of A. (4 marks)

vi. Solve the system using the

-factorization method. (3 marks)

vii. Solve the system using Cramer's Rule. Check that your answer coincides with your answer in part (vi). (5 marks)

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