Name: Date: Period:

Matrices Quiz #2 _____7.4: Perform and describe operations with matrices my hand and using a calculator. 1) Calculate the following:

2) Matrix W =

Matrix Y =

Is it possible to perform the matrix operation W x Y? Explain why or why not! If possible, what will the dimensions of the new matrix be? Explain how you know: If possible, write the matrix W x Y (If impossible, do not answer). You may check on your calculator, but you must show how at least one of the numbers in the product was calculated.

3) Matrix C =

Matrix D =

Is it possible to perform the matrix operation C x D? Explain why or why not! If possible, what will the dimensions of the new matrix be? Explain how you know: If possible, write the matrix A x B (If impossible, do not answer). You may check on your calculator, but you must show how at least one of the numbers in the product was calculated. 4) For any two matrices, is 𝐴𝐵 = 𝐵𝐴? Use an example from above to justify why or why not:

_____7.5: Solve systems with more than three variables using row operations and technology, and determine the number of solutions to a system: 1. The matrices below are augmented matrices representing systems of equations. Based on the matrices, determine whether the equation has exactly one solution, inconsistent, or dependent. If there are solutions, represent them all:

2. Solve the system of equations using matrices. Show your steps clearly!! You can still get credit, even if you make a small mistake!

3. Using your calculator, determine how many solutions the system below has and explain how you know.

Represent the solution to the system of equations above:

_____7.6: Find inverses of matrices and use them to solve problems: 1. Find the inverse of the matrix above by hand:

2. Find the inverse of the matrix below using a calculator:

3. Explain why the inverse of the following matrix does not exist:

3. Solve the matrix equation below for A:

𝐴 ∗ 𝑋 = 𝐶