Hw04_Sol_Su09

# Hw04_Sol_Su09 - ECE220 Homework#4 Solutions Solution to...

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Unformatted text preview: ECE220 Homework #4 Solutions Solution to Problem 5.4 Here, x = [2 , 1 , α, 3 ,- 4] and y = [ α,- 3 , 2 ,- 1 , 1] So, x.y = 2 α + (- 3) + 2 α + (- 3) + (- 4) = 4 α- 10 ⇒ 0 = 4 α- 10 ⇒ α = 2 . 5 Solution to Problem 5.10 1. C 1 = AB = 2- 1- 1- 2 1 1- 1 3 2- 1 1 The multiplication is not legal in this case as the number of columns in A are not equal to number of rows in B. 2. C 2 = AB T = 2- 1- 1- 2 1 3- 1 1 2 1- 1 The multiplication is not legal in this case as the number of columns in A are not equal to number of rows in B T . 3. C 3 = A T B = 2- 1- 1- 2 1 1- 1 3 2- 1 1 =- 1- 2- 1- 4 4. C 4 = A T B T = 2- 1- 1- 2 1 3- 1 1 2 1- 1 = 1 4- 3 1- 2- 1 Solution to Problem 5.20 Consider the matrix [ A | I ]: 1 1- 1 1 1 1 2 1 2 4 1 . Swap Rows 1 & 2 1 1 2 1 1- 1 1 2 4 1 . Row 1 ← 2*Row 1 - Row 3 2 2- 1 1- 1 1 2 4 1 . Row 2 ← Row 1 - 2*Row 2 2 2- 1 2- 2 2- 1 2 4 1 . Row 3 ← Row 2 - Row 3 2 2- 1 2- 2 2- 1- 4- 2 2- 2 . Row 1 ← 0.5*Row 1, Row 2 ← 0.5*Row 2, Row 3 ← (-0.25)*Row 3 1 1- . 5 1- 1 1- . 5 1 . 5- . 5 . 5 . Therefore, A- 1 = 1- . 5- 1 1- . 5 . 5- . 5 . 5 ....
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Hw04_Sol_Su09 - ECE220 Homework#4 Solutions Solution to...

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