Matrix Unit Test Review

Random

100

Identify element a₂₃ from A =

2

200

Find the determinant:

[[6,4],[-9,3]]

54

300

This matrix has the same number of rows as columns.

Square Matrix

400

Find all three separate determinants:

[[-4,3],[-1,2]] , [[6,4],[-2,3]], and [[-8,-5],[3,0]]

-5, 26, and 15

500

Write a 4x4 identity matrix

[[1,0, 0,0],[0,1, 0,0],[0,0,1,0],[0,0,0,1]]

Inverses

100

How do you know if two matrices are inverses?

When you multiply them together, their product equals an Identity matrix.

200

Will the following matrix have an inverse? How do you know?

[[3, 3],[-1, -1]]

No it will not have an inverse. You know because the determinant is zero.

300

What is the inverse of 

[[3,2],[4,1]]

[[-1/5,2/5],[4/5,-3/5]]

400

Find the inverse of the following matrix:

[[3, 4],[-2, -1]]

[[-1/5, -4/5],[2/5, 3/5]]

500

Are the following matrices inverse? How do you know?

[[12, 4, -7],[-2, -1, 5],[3, -8, 6]] and [[-12, -4, 7],[2, 1, -5],[-3, 8, -6]]

No, because when you multiply them together, it will not make an Identity matrix.

Systems of Equations

100

What is the matrix from of 

{[2x+3y=8], [4x-y=5]}

[[2,3],[4,-1]][[x],[y]]=[[8],[5]]

200

What is the solution of the matrix equation

[[5,3],[2,1]][[x],[y]]=[[-5],[1]]

[[2],[-5]]

300

What is the solution of

[[-6,-3],[8,4]][[x],[y]]=[[144],[-64]]

no solution

400

Solve the System using matrices

4x - y = 19

5x - 5y = 20

(5, 1)

500

Solve the following using matrices

5x - 2y = 18

3x - y = 7

x=-4

y=-19

Addition and Subtraction

100

What is the rule for determining if two matrices can be added or subtracted together?

The matrices have to be the exact same dimensions (equal number of rows and columns)

200

Simplify the following matrices based problem:

300

Given Matrix X and Matrix Y. What is Y-X?

Matrix X=

[[2,-3],[-1,4]]

Matrix Y=

[[-4,1],[3,-2]]

[[-6,4],[4,-6]]

400

Subtract:

[[1,-2, -1],[-3, 4, 3],[5, -6, -5]] - [[-2, 1, 2], [4, 3, -4], [-6, -5, 6]] 

[[3,-3,-3],[-7,1,7],[11,-1,-11]]

500

2C + A

What is 

|7  -19|

|0  15|

Matrix Multiplication

100

Can the following matrices be multiplied together? How do you know? 

[[1,2],[3, 4],[5, 6]] [[1,2, 3],[4, 5, 6]]

Yes, because the first matrix is a 3x2, and the second matrix is a 2x3. Since the second matrix has the same number of rows, as the first one has columns (2), these matrices can be multiplied together.

200

Solve the following operations:

2[[1,-2],[-3, 4],[5, -6]] + [[-7,8],[9, -10],[-11, 12]] 

[[-5,4],[3,-2],[-1,0]]

300

What is AxB?

Matrix A=

[[1,1],[1,1]]

Matrix B= 

[[0,3],[4,4]]

[[4,7],[4,7]]

400

What is AxB?

matrix A=

[[4,3],[9,7]]

matrix B=

[[6,3],[9,4]]

[[51,24],[117,55]]

500

Solve the following multiplication:

[[1,2, -2, -1],[-3, -4, 4, 3]] xx [[5],[6],[7],[8]] 

[[-5],[13]]