MATH221 December 2011
• Q1 (a) • Q1 (b) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 • Q8 (a) • Q8 (b) •
Question 02 (b)
Compute A-1 when t = 0, where
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint.
There are several ways to compute the inverse of a matrix. Which ones are you familiar with?
One way to obtain the inverse of a matrix is to row-reduce the augmented matrix [A | I]. Here I is the 3x3 identity matrix.
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When t = 0, the matrix A is
One way to obtain the inverse of a matrix is to row-reduce the augmented matrix [A|I]. Let's proceed with this method.
Perform L2 → L2-L1 and L3 → L3-(2/3)L1
Perform L3 → 3L3
Perform L3 → L3-L2
Perform L3 → (-1)L3
Perform L1 → L1-L2 and L2 → L2+2L3
Perform L1 → L1-5L3
Perform L1 → (1/3)L1 and L2 → (1/2)L2
And we can conclude that