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MATH1144 Matrix/Question.txt**]**

MATH1144 – Calculus and Analysis 2

1. Use row reduction to find all solutions to the following system of equations and

write the solutions as a sum of three vectors:

-3x + y + 3z – w = -3

x – 2y – z + w = 3

-2x – y + 2z = 0.

2. Consider the matrix

B =

?

?

2 1 3

3 2 3

4 4 2

?

? .

(a) Show, by calculating det B, that B has an inverse B-1?

(b) Use elementary row operations in the augmented matrix [B : I] to find the

inverse B-1.

(c) Check your result of part b). by showing that B-1B = I.

(d) Use your results above to find the solution of the system of equations:

2x + y + 3z = -1

3x + 2y + 3z = 0

4x + 4y + 2z = 2.

(6 + (2 + 6 + 3 + 3) = 20 marks)