Question1
A 2X2 matrix A is given by,
a b
c d
Given that a = 9, b = -1, c = 4 and d = 5, determine the entry in the first row, second column of the inverse A-1. Give your answer to 3 decimal places.
Answer
Question 2
A 2X2 matrix M is given by
a b
0 d
Write down the larger eigenvalue of the matrix 40M where a =2, b=6 and d=15.
Answer
Question 3
A 3X3 matrix is found to have 8 as one of its eigenvalues. It is required to find its eigenvector v = (x1, x2, x3)T.
The corresponding eigenvector equations are
-1.2×2 – x3 = 0,
2×1 + -1.2×2 = 0, and
2×1 + x3 = 0.
One possible eigenvector was found to be (1, k, -2)T
What is the value of k? Give your answer to 3 decimal places.
Answer
Question 4
If a 3X3 matrix M has characteristic equation 1λ3 + -21λ2 + 5λ = 0.
What is the value of the larger non-zero eigenvalue of M? It is not required to know M exactly.Give your answer to 3 decimal places.
Answer
Question 5
M is a 2X2 singular matrix with tr M = 106. What is the value of the smaller eigenvalue of M? It is not necessary to know M exactly.
Answer
Question 6
A 2X2 matrix M is given by
a b
c d
Given that a = 9, b = 27 and c = 32, what is the value of d such that the matrix M is singular.
Give your answer to the nearest integer.
Answer
Question 7
A system of simultaneous equations in terms of three unknowns, x1, x2 and x3, was solved using Gauss Elimination Method. The final augmented matrix in upper triangular form was given by,
1 a b 8
0 c 3 22
0 0 d 6
When a = -4, b = 4, c = 1 and d = 4, using back substitution, calculate the value of x1, giving your answer to 3 decimal places.
Answer