Week+2+&+3

[] **[|Matrix review.ppt]**  Note of Matrix Review Step 1: Write the system as a matrix equation. Step 2: Find the inverse of the coefficient matrix.  Note: This can be done easily for a 2 x 2 matrix. For larger matrices, use a calculator to find the inverse. Step 3: Multiply both sides of the matrix equation by the inverse.(The inverse of the coefficient matrix times the coefficient matrix equals the identity matrix.)  Note: The multiplication order on the right side is very important. We cannot multiply a 3 x 1 times a 3 x 3 matrix!

**Name:** Yanhua Ma **Score:** 4 / 4 points (100%) Using Matrices to Solve Systems of Equations

//Identify the choice that best completes the statement or answers the question.// || || a. || || c. ||  ||
 * **Multiple Choice**
 * ||  || //Write a matrix equation for the given systems of equations.// ||
 *  || 1. || [[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc001-1.jpg width="100" height="71" align="top" caption="mc001-1.jpg"]] 
 * b. || [[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc001-3.jpg width="179" height="89" align="middle" caption="mc001-3.jpg"]] || d. || [[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc001-5.jpg width="179" height="89" align="middle" caption="mc001-5.jpg"]] ||


 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**ANSWER:** || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">C <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">The matrix equation is (coefficient matrix) · (variable matrix) = constant matrix. ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**POINTS:** || 1 / 1 ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**FEEDBACK:** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> Correct! ||

|| a. || || c. ||  ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt; text-align: right;">2. || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">[[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc002-1.jpg width="73" height="61" align="middle" caption="mc002-1.jpg"]] <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt; text-align: right;">2. || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">[[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc002-1.jpg width="73" height="61" align="middle" caption="mc002-1.jpg"]] <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">
 * b. || [[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc002-3.jpg width="136" height="67" align="middle" caption="mc002-3.jpg"]] || d. || [[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc002-5.jpg width="147" height="67" align="middle" caption="mc002-5.jpg"]] ||


 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**ANSWER:** || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">D <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">A matrix equation is (coefficient matrix) · (variable matrix) = constant matrix. ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**POINTS:** || 1 / 1 ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**FEEDBACK:** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> Correct! ||

|| a. || (–4, 1) || c. || (, 1) ||
 * ||  || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">//Solve the matrix equation by using inverse matrices.// ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt; text-align: right;">3. || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">[[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc003-1.jpg width="154" height="67" align="middle" caption="mc003-1.jpg"]] <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt; text-align: right;">3. || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">[[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc003-1.jpg width="154" height="67" align="middle" caption="mc003-1.jpg"]] <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">
 * b. || (–4, [[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc003-2.jpg width="22" height="15" align="bottom" caption="mc003-2.jpg"]]) || d. || ([[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc003-4.jpg width="19" height="46" align="middle" caption="mc003-4.jpg"]], [[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc003-5.jpg width="15" height="15" align="bottom" caption="mc003-5.jpg"]]) ||


 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**ANSWER:** || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">A <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">Write a matrix equation for the system of equations. Then, find the inverse of the coefficient matrix. Finally, multiply each side of the matrix equation by the inverse matrix. ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**POINTS:** || 1 / 1 ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**FEEDBACK:** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> Correct! ||

|| a. || (, 2) || c. || ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt; text-align: right;">4. || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">[[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc004-1.jpg width="162" height="67" align="middle" caption="mc004-1.jpg"]] <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt; text-align: right;">4. || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">[[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc004-1.jpg width="162" height="67" align="middle" caption="mc004-1.jpg"]] <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">
 * b. || (–5, [[image:http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/solvingbyinverse_files/mc004-3.jpg width="14" height="15" align="bottom" caption="mc004-3.jpg"]]) || d. || (–5, 2) ||


 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**ANSWER:** || <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">D <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 12pt;">Write a matrix equation for the system of equations. Then, find the inverse of the coefficient matrix. Finally, multiply each side of the matrix equation by the inverse matrix. ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**POINTS:** || 1 / 1 ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;">**FEEDBACK:** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 12pt;"> Correct! ||