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# 2201NSC Maths For The System Of Equations Described By The Augmented Matrix

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• Course Code: 2201NSC
• University: Griffith University
• Country: Australia

## Questions:

Q1 (a) Write the system of equations
2x − 2y − z = 1
2x + y + 2z = 1
4x + 3y + 5z = 2
as a product
Ax = b
(b) Solve for x, y and z using Gaussian elimination.
(c) Find det A [show your working].
(d) Explain why det A is consistent with your solution in part (b).
(e) For what values of c is the matrix
c −2 −1
4 3 5
2 1 c
singular?

Q2 (a) Write the system of equations
x + y + 2z = 2
2x + y + 2z = 1
4x + 3y + 5z = 2
as a product
Ax = b
(b) Find A−1 using Gaussian elimination, and use it to solve for x, y, z.
(c) Confirm your solution using Cramer’s rule [show your working].
(d) Explain why det A is consistent with your solutions in part (b).
(e) Given the block matrix
A =
I 0 0
0 I 0
B C I
for matrices 0, I, B, C ∈ R n×n
determine A−1
in block form [use Gaussian elimination in block form

Q3 We can use methods from linear algebra to find polynomial fits through data points, and learn about the nature of such fits. In this problem we will find the quadratic y = ax2 + bx + c that passes through specific points.
(a) Show that, for a quadratic passing though the three points (x1, y1),(x2, y2) and (x3, y3), the coefficients for the quadratic y = ax2 + bx + c satisfy a
system of equations described by the augmented matrix.

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