MATH1144 – Calculus and Analysis 2

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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)

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