Chapter 6 Assessment

Master linear algebra! Solve matrix problems, systems of equations, and linear programming challenges.

Matrix Dimensions Match each matrix with its dimensions: 1 x 3 5 x 5 4 x 1 5 x 2 Multiply the matrices together and put your answers in the corresponding parts of the table. 6 0 -27 12 Multiply the matrices together and put your answers in the corresponding parts of the table. -30 24 15 -12 Multiply the matrices together and put your answers in the corresponding parts of the table. -5 -10 8 13 17 -17 -28 -34 -74 74 32 -52 52 Solve the following question using Cramer's Rule. Then fill in the blanks to answer.4x - 3y = -6x + 2y = -7 The determinant of the coefficient matrix is 11. When solving for x, the determinant of the numerator is -33. When solving for y, the determinant of the numerator is -22. Therefore the final answer is (-3, -2) Find the inverse of the matrix shown below. Be sure to multiply in your scalar (1 2.5 -3 -1.5 -2 When solving the following equation by inverse matrices, which of the following would be the determinant of matrix A (coefficient matrix)?2x - y = 12x + 3y = 13 8 4 -8 -4 When solving the following equation by inverse matrices (same question as above), which of the following would be the inverse of matrix A?2x - y = 12x + 3y = 13 Continue solving the previous problem using the inverse matrices process. Fill in the blanks. The fraction out front (that will be multiplied in last) is 1 After multiplying the two matrices together the number in the top row is 16. The number in the bottom row is 24. The final answer (in ordered pair format) is (2, 3). Find the determinant of the following -53 -25 -15 -3 Find the partial fraction decomposition for the following fraction: Use a slash to enter your fractions for example:would be recorded as 1 + 5) A batch of Mango Sunrise using 3 liters of mango juice and 1 liter of strawberry juice. A batch of Oasis Dream using 2 liters of mango juice and 1 liter of strawberry juice. The store has 40 liters of mango juice and 15 liters of strawberry juice that it wants to use up before the end of the day. Fill in the table to write the constraints. If x represents the batches of Mango Sunrise and y represents the batches of Oasis Dream.For the ≥ symbol you can use the combination "> or =" Restriction for batches of Mango Sunrise x > or = 0 Restriction for batches of Oasis Dream y > or = 0 Restriction for mango juice 3x + 2y < or = 40 Restriction for strawberry juice x + y < or = 15 Find the Maximum Value Only for the following set of inequalitiesx ≥ 0y ≥ 02x + 3y ≤ 6x + y ≤ 8