Random
Inverses
Systems of Equations
Addition and Subtraction
Matrix Multiplication
100
Identify element a23 from A =
2
100
How do you know if two matrices are inverses?
When you multiply them together, their product equals an Identity matrix.
100
What is the matrix from of
{[2x+3y=8], [4x-y=5]}
[[2,3],[4,-1]][[x],[y]]=[[8],[5]]
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)
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
Find the determinant:
[[6,4],[-9,3]]
54
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.
200
What is the solution of the matrix equation
[[5,3],[2,1]][[x],[y]]=[[-5],[1]]
[[2],[-5]]
200
Simplify the following matrices based problem:
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
This matrix has the same number of rows as columns.
Square Matrix
300
What is the inverse of
[[3,2],[4,1]]
[[-1/5,2/5],[4/5,-3/5]]
300
What is the solution of
[[-6,-3],[8,4]][[x],[y]]=[[144],[-64]]
no solution
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]]
300
What is AxB?
Matrix A=
[[1,1],[1,1]]
Matrix B=
[[0,3],[4,4]]
[[4,7],[4,7]]
400
Find all three separate determinants:
[[-4,3],[-1,2]] , [[6,4],[-2,3]], and [[-8,-5],[3,0]]
-5, 26, and 15
400
Find the inverse of the following matrix:
[[3, 4],[-2, -1]]
[[-1/5, -4/5],[2/5, 3/5]]
400
Solve the System using matrices
4x - y = 19
5x - 5y = 20
(5, 1)
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]]
400
What is AxB?
matrix A=
[[4,3],[9,7]]
matrix B=
[[6,3],[9,4]]
[[51,24],[117,55]]
500
Write a 4x4 identity matrix
[[1,0, 0,0],[0,1, 0,0],[0,0,1,0],[0,0,0,1]]
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.
500
Solve the following using matrices
5x - 2y = 18
3x - y = 7
x=-4
y=-19
500
2C + A
What is
|7 -19|
|0 15|
500
Solve the following multiplication:
[[1,2, -2, -1],[-3, -4, 4, 3]] xx [[5],[6],[7],[8]]
[[-5],[13]]