CEE 470_HW1.pdf - Prof X.S Zhang Spring 2019 CEE 470...

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Prof. X.S. Zhang Spring 2019 1 CEE 470 Homework # 1 Due Wednesday January 23, 2pm Write your name and ID on the cover page Question 1 (20 pts) Read Appendices A and B of Felippa’s book (available on Compass2g) and class notes on vectors and matrices files: Note 1 - vector review.pdf Note 2 - matrix review.pdf They are posted on the Compass webpage of the course. Answer the following questions: 1. Find dot(inner) product and outer(matrix) product of vector a and b, where ? = [ 1 −2 7 ] ? = [ 3 8 1 ] 2. Give 3 by 3 (not just the zero matrix) examples of a. Symmetric matrix b. Lower triangular matrix c. Anti-symmetric matrix (aka. Skew symmetric) 3. Which of the following matrices are guaranteed to equal (A+B) 2 ? Show your work. A 2 + 2AB + B 2 , A(A+B) + B(A+B), (A+B)(B+A), A 2 +AB+BA+B 2 4. One way to visualize matrix vector multiplication c = Ab is that c is the linear combination of columns of A using coefficients in b. Use the following matrix and vector to check this rule.
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