solutions_9.pdf - Homework MA 213 Due 2014-Nov-17 You may...

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Homework, MA 213 Due: 2014-Nov-17 You may work with others to figure out how to do questions, and you are welcome to look for answers in the book, online, by talking to someone who had the course before, etc. However, you must write the answers on your own. You must also show your work (you may, of course, quote any result from the book). 1. Find the determinant. (a) 1 4 2 8 The formula for 2 × 2 determinants gives 1 · 8 - 2 · 4 = 0. (b) 2 1 1 1 1 0 6 4 1 Gauss’s Method - (1 / 2) ρ 1 + ρ 2 -→ - 3 ρ 1 + ρ 3 - 2 ρ 2 + ρ 3 -→ 2 1 1 0 1 / 2 - 1 / 2 0 0 - 1 followed by multiplying down the diagonal gives the determinant as - 1. 2. Consider the linear transformation t : R 3 R 3 represented with respect to the standard bases by this matrix. 1 0 - 1 3 1 1 - 1 0 3 (a) Compute the determinant of the matrix. Gauss’s Method - 3 ρ 1 + ρ 2 -→ ρ 1 + ρ 3 1 0 - 1 0 1 4 0 0 2 gives the determinant as 2. (b) Find the size of the box defined by these vectors.
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