MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 MAC 0 Module 0 Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the system by using Gaussian elimination with backward substitution or by reducing the matrix to reduced-row echelon form. ) x - y + z = x + z = 0 x + y + z = -0 A) (0, -, ) (0, -, 0) No solution (0, 0, -) Objective: (9.) Solve Linear System in Two/Three Variables with Matrices ) Acme Electronics is a company which makes computer chips. The following table gives the revenue, y, in dollars for this company during the three stated years, x. In this table x = 0 corresponds to 90, while x = 6 corresponds to 96. x 0 6 y,000 7,99,0,96 This set of data can be modeled by f(x) = ax + bx + c, where x represents the year. Find a linear system for which the solution represents the values of a, b, and c. Use technology to solve this system. Then, using the quadratic equation, predict the revenue for the year x =. Round your answer to the nearest hundred dollars.. A) $,,00 $,,00 $,,00 $,0,00 Objective: (9.) Solve Apps: Linear Systems with Three Variables Determine if the matrix is in row-echelon form. -7 ) A) No Yes Objective: (9.) Determine Whether Matrix is in Row-Echelon Form (Y/N) State the dimensions of the matrix. ) - -6 A), -, -6,,, 6 Objective: (9.) State Dimension of Matrix

2 The augmented matrix is in row-echelon form and represents a system of linear equations. Solve the system using backward substitution ) 0 Write the solution as an ordered triple, if possible. 0 0 A) (, -7, ) No solution (-, -6, ) (, -6, ) Objective: (9.) Solve Linear System from Augmented Matrix in Row-Echelon Form Perform the matrix operation. 6) Let C = - and D = - A) Find C - D Objective: (9.) Add, Subtract, Find Scalar Multiples of Matrix Find the values of the variables. 7) 7-6 = x y -6 m A) x =, y = 7, m = -6 x = 7, y =, m = -6 x = -7, y =, m = 6 x = -7, y = -, m = 6 Objective: (9.) Solve for Variables in Matrix Equation ) Consider the following simplified digital photograph that has a grid with four gray levels numbered from 0 to. It shows a letter Y in black on a light gray background. Let A be the matrix that represents this figure digitally. Find the matrix B for which B - A represents the negative image of the picture represented by A. A) Objective: (9.) Solve Apps: Matrices and Digital Photography

3 Find the values of the variables. 9) 0 - = m- n+ x 0 0 A) m = -9, n =, x = 0 m = -, n = 9, x = - m = 0, n = -, x = m =, n = -9, x = Objective: (9.) Solve for Variables in Matrix Equation Perform the matrix operation. 0) Let A = 6 and B = 0-6 A) 7 7. Find A + B. Objective: (9.) Add, Subtract, Find Scalar Multiples of Matrix ) Let C = A) - -. Find C Objective: (9.) Add, Subtract, Find Scalar Multiples of Matrix ) Matt bought pounds of oranges and pounds of apples and paid $.6, before tax. Andy bought pounds of oranges and pounds of apples and paid $.6, before tax. Use this information to set up a matrix equation of the form AX = B, which can be solved to determine the price per pound for oranges and apples. Solve this matrix equation to find the price per pound of apples. Use the fact that for A =, A- = -. - A) $0.9 per pound $0.9 per pound $0.9 per pound $0. per pound Objective: (9.6) Solve Apps: Linear System with More Than Two Variables Write the system in the form AX = B. Then solve the linear system by computing X = A-B with a calculator. Round numbers to the nearest tenth, as necessary. ).x +.y -.z + 0.6w =.7 6.x - 0.z -.w = 0..y -.w = 0.0x +.0y -.z = 9 A) X = X = X = Objective: (9.6) Tech: Solve Linear System Using Inverse of Coefficient Matrix X =

4 Find A- without a calculator. 0 0 ) A = A) A- = A- = Objective: (9.6) Find Inverse of Matrix Without Calculator A- = Determine whether the matrices are inverses. ) 6 - -, A) Yes No Objective: (9.6) Determine If Matrices are Inverses of Each Other Determine if matrix A is invertible. 6) A = -9 0 A) Not invertible Invertible Objective: (9.7) Determine If Matrix is Invertible Using Determinant Use technology to calculate det A ) A = 6 9 A) Objective: (9.7) Tech: Find Determinant of Matrix Find the specified minor and cofactor for the matrix A. - ) M and A if A = - 7 A) M = 0 and A = - 0 M = - and A = - M = 0 and A = 0 M = and A = Objective: (9.7) Find Minor, Cofactor of Given Element in Matrix

5 Find the area of the figure using determinants. 9) y (, ) (, (-, -) - - x A) Objective: (9.7) Find Area Using Determinant Find det A using the method of cofactors ) A = A) Objective: (9.7) Find Determinant of Matrix Using Cofactors