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Homework 4 Solution

# Homework 4 Solution - MAT 242 Written Homework#4 EP2.2...

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MAT 242 Written Homework #4 SOLUTIONS EP2.2 — 2.4/H3.1 — 3.3 Due: February 13/ Solve the following problems, showing any necessary work. This includes row operations. 1. [1 point] Solve the following system of linear equations using Cramer’s Rule. 4 x + y = - 1 3 x + 2 y = 5 Solution: This is the system of linear equations AX = B , where A = 4 1 3 2 and B = - 1 5 . det A = 4 1 3 2 = 4 · 2 - 1 · 3 = 5 det A 1 [ B ] = - 1 1 5 2 = ( - 1) · 2 - 1 · 5 = - 7 det A 2 [ B ] = 4 - 1 3 5 = 4 · 5 - ( - 1) · 3 = 23 x = x 1 = det A 1 [ B ] det A = - 7 5 y = x 2 = det A 2 [ B ] det A = 23 5 2. Evalute - 9 4 0 0 4 - 2 0 2 - 8 6 - 4 0 6 - 3 0 2 a. [1 point] . . . using Expansion by Minors (at least once). Solution: The easiest way is to expand by minors along the third column, then use Sarrus’s Method: - 9 4 0 0 4 - 2 0 2 - 8 6 - 4 0 6 - 3 0 2 = 0 · | * | - 0 · | * | + ( - 4) · - 9 4 0 4 - 2 2 6 - 3 2 - 0 · | * | = ( - 4) · [( - 9)( - 2)(2) + (4)(2)(6) + (0)(4)( - 3) - (0)( - 2)(6) - (4)(4)(2) - ( - 9)(2)( - 3)] = ( - 4) · [36 + 48 - 32 - 54] = ( - 4)( - 2) = 8 . = 1

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b. [1 point] . . . using Gaussian Elimination.
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