3-8 Solving Systems of Equations Using Inverse Matrices. Determine whether each pair of matrices are inverses of each other. 13.
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1 13. Determine whether each pair of matrices are inverses of each other. If K and L are inverses, then. Since, they are not inverses. 15. If P and Q are inverses, then. Since, they are not inverses. esolutions Manual - Powered by Cognero Page 1
2 17. Find the inverse of each matrix, if it exists. Since the determinant does not equal 0, the inverse exists. esolutions Manual - Powered by Cognero Page 2
3 19. Since the determinant does not equal 0, the inverse exists. esolutions Manual - Powered by Cognero Page 3
4 21. Since the determinant does not equal 0, the inverse exists. esolutions Manual - Powered by Cognero Page 4
5 23. Since the determinant does not equal 0, the inverse exists. esolutions Manual - Powered by Cognero Page 5
6 25. Since the determinant does not equal 0, the inverse exists. CCSS PERSEVERANCE Use a matrix equation to solve each system of equations. 27. x + y = 4 x + y = 4 Since the determinant is equal to 0, the inverse does not exist. Therefore, the system has no solution. esolutions Manual - Powered by Cognero Page 6
7 29. The matrix equation is Find the inverse of the coefficient matrix.. Multiply each side of the matrix equation by the inverse matrix. The solution is ( 1, 5). esolutions Manual - Powered by Cognero Page 7
8 31. y x = 5 2y 2x = 8 Rewrite the given system as below. x + y = 5 2x + 2y = 8 Since the determinant is equal to 0, the inverse does not exist. Therefore, the system has no solution. esolutions Manual - Powered by Cognero Page 8
9 y 0.2x = 1 0.4y 0.1x = 0.5 Rewrite the given system as below. 0.2x + 1.6y = 1 0.1x + 0.4y = 0.5 The matrix equation is. Find the inverse of the coefficient matrix. Multiply each side of the matrix equation by the inverse matrix. The solution is ( 5, 0). esolutions Manual - Powered by Cognero Page 9
10 35. 2y 4x = 3 4x 3y = 6 Rewrite the given system as below. 4x + 2y = 3 4x 3y = 6 The matrix equation is. Find the inverse of the coefficient matrix. Multiply each side of the matrix equation by the inverse matrix. The solution is. esolutions Manual - Powered by Cognero Page 10
11 47. Evaluate each determinant. 49. Rewrite the first two columns to the right of the determinant. Find the products of the elements of the diagonals. Find the sum of each group. Subtract the sum of the second group from the sum of the first group. The value of the determinant is 551. esolutions Manual - Powered by Cognero Page 11
12 51. Find each product, if possible. 53. MILK The Yoder Family Dairy produces at most 200 gallons of skim and whole milk each day for delivery to large bakeries and restaurants. Regular customers require at least 15 gallons of skim and 21 gallons of whole milk each day. If the profit on a gallon of skim milk is $0.82 and the profit on a gallon of whole milk is $0.75, how many gallons of each type of milk should the dairy produce each day to maximize profits? Let x be the number of gallons of skim milk. Let y be the number of gallons of whole milk. The optimize function is. Graph the inequalities in the same coordinate plane. The vertices of the feasible region are (15, 185), (15, 21), and (179, 21). To maximize the profit, the dairy has to produce 179 gallons of skim milk and 21 gallons of whole milk. esolutions Manual - Powered by Cognero Page 12
13 Identify the type of function represented by each graph. 55. The graph is in a V shape. So, it represents an absolute value function. esolutions Manual - Powered by Cognero Page 13
SOLUTION: Because the fractions have a common denominator, compare the numerators. 5 < 3
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