Random
Addition and Subtraction
Matrix Multiplication
Inverses
Systems of Equations
100
What the the order of the matrix
2x3
100
What is the rule for determining if two matrices can be added or subtracted together?
The matrices have to be the exact same order (equal number of rows and columns)
100
If you are able, how do you multiply matrices?
You multiply each row in the first matrix by each column in the second matrix and then add each of those products together to get each individual element in the solution matrix.
100
What is the formula for finding the inverse of a 2x2 matrix:
A=[[a,b],[c,d]]
A^-1=1/(ad-bc)[[d,-b],[-c,a]]
100
When will a system of equations have no solutions?
When the determinant = 0 (i.e. it is not possible to find an inverse)
200
Identify element a23 from A =
2
200
Find A - B:
A = [[2,-3],[-1,4]]
B=[[-4,1],[3,-2]]
A-B=[[-6,4],[4,-6]]
200
Multiply A and B.
A=[[1,1],[1,1]]
B=[[0,3],[4,4]]
AB=[[4,7],[4,7]]
200
Determine if these two matrices are inverses:
A=[[-9,-4],[-5,-2]]
B=[[1,-2],[-5/2,9/2]]
Yes, they are!
200
Write a matrix to represent the following network:
[[0,1,1,1,0],[1,0,1,0,1],[1,1,0,0,1],[1,0,0,0,0],[0,1,1,0,0]]
300
Identify
1. 2x2 identity matrix
2. 3x3 identity matrix
1. [[1,0],[0,1]]
2.[[1,0,0],[0,1,0],[0,0,1]]
300
Find B - A
[[0,4,1],[2,-3,0],[6,6,-2]]
300
Multiply:
[[1,2, -2, -1],[-3, -4, 4, 3]] [[5],[6],[7],[8]]
[[-5],[13]]
300
Find the determinant of A:
A=[[3, 3],[-1, -1]]
det(A) = 0
300
Solve these simultaneous equations using matrix inverses, expressing your answers to 4 decimal places:
6x - 3y = -1
8x - 5y = -2
x=0.1667 and y=0.6667
400
Do the following, and determine a13 of result:
[[-25,-30,20],[-20,10,5]]
a13 = 20
400
Find -1/3 B - A
[[4,12,-8],[23,-17,12],[-1,10,-6]]
400
Multiply:
[[-12,-3,-6,12,6],[4,-4,0,0,0]]
400
If possible, find the inverse of A:
A=[[2,6],[-1,-5]]
A^-1=[[5/4,3/2],[-1/4,-1/2]]
400
Solve these simultaneous equations using inverse matrices, expressing your answers as fractions:
-4x - 7y = 2
5x - y = 7
x=47/39 and y=-38/39
500
Can the following matrices be multiplied together? If so, what would the size of the solution matrix be? If not, explain why not?
[[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. Their product matrix would have 3 rows and 3 columns.
500
Find 2A-1/6 B
[[2,3],[-11,7],[-18,-20],[-3,18]]
500
Multiply:
[[6,-8,2],[7,-5,11],[-2,6,-10]]
500
If possible, find the inverse of A:
A=[[3, 4],[-2, -1]]
A^-1=[[-1/5, -4/5],[2/5, 3/5]]
500
Solve using inverse matrices, expressing your answers to 3 significant figures:
x=-0.714 , y=4.86 , and z=-0.714