Science:Math Exam Resources/Courses/MATH152/April 2012/Question 06 (b)

MATH152 April 2012

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Question 06 (b)
This question requires little or no calculations. If $A=C^{-1}BC$, where C is an invertible matrix, and det B=12, det C=-3. Calculate det A.

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!

Hint
If$A=C^{-1}BC$, then $A$, $B$ are similar matrices.

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Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. By the equation $A=C^{-1}BC$, we can see that $A,B$ are similar matrices. One of the properties of similar matrices is that their determinants are equal. Hence, ${\color {blue}\operatorname {Det} (A)=\operatorname {Det} (B)=12}$