MATH152 April 2013
• QA 1 • QA 2 • QA 3 • QA 4 • QA 5 • QA 6 • QA 7 • QA 8 • QA 9 • QA 10 • QA 11 • QA 12 • QA 13 • QA 14 • QA 15 • QA 16 • QA 17 • QA 18 • QA 19 • QA 20 • QA 21 • QA 22 • QA 23 • QA 24 • QA 25 • QA 26 • QA 27 • QA 28 • QA 29 • QA 30 • QB 1(a) • QB 1(b) • QB 1(c) • QB 1(d) • QB 2(a) • QB 2(b) • QB 2(c) • QB 2(d) • QB 3(a) • QB 3(b) • QB 3(c) • QB 4(a) • QB 4(b) • QB 4(c) • QB 5(a) • QB 5(b) • QB 5(c) • QB 6(a) • QB 6(b) • QB 6(c) •
Question A 12
Calculate the following whenever defined. Otherwise state undefined and include a brief explanation.
A matrix such that where is the identity matrix.
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Proceed similarly to question A11. Start off with a general matrix
and perform the multiplication.
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We proceed as in the hint. Let
Then we have
Looking at the first row on the matrices on the left and right gives
and this is inconsistent since the last two imply that both a and b are zero and this contradicts the first line. Thus no such matrix D exists.
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