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Homework for §3.4 Let 1 2 1 3 0 2 A = 9 3 6 and B = 1 −1 3 . 2 1 4 −2 1 9 1. Calculate 3A + B. 2. Calculate 4A − 2B. ......................................................................................... Find the following matrix products −1 6 2 3 3. 9 4 0 1 −1 9 2 0 3 4. 0 2 1 0 2 −1 3 2 3 1 9 −1 4 5. −1 −1 2 −3 2 0 3 0 2 1 3 1 ......................................................................................... 6. Let A= a b c d . Find a 2 × 2 matrix L such that LA = a b c + ka d + kb . This shows that the elementary row operations can be thought of as a sequence of left multiplications by certain matrices. Proceed as follows: ka kb . (Multiply the 1st row by k) (a) Find L1 such that L1 A is c d ka kb . (Add the 1st row to the 2nd row) (b) Find L2 such that L2 (L1 A)) is c + ka d + kb a b (c) Find L3 such that L3 (L2 (L1 A)) is . (Divide the first row by k) c + ka d + kb Then L = L3 L2 L1 .