Matrices
Scalar and Elements
Operation on matrices
Determinant
Inverse
100
***Triple Play***
The term used to refer to the number of rows and columns in a matrix.
Order of a matrix
or
Dimension of a Matrix
100
Identify element a23 from A =
What is a23 = 2
100
Simplify the following:
100
Find the determinant:
[[6,4],[-9,3]]
What is 54
100
**Daily Double**
How do you get the inverse of a matrix?
(1/det)*[[b2, -b1],[-a2, a1]]
200
The requirement when multiplying matrices.
The number of columns of the first matrix must equal the number of rows of the 2nd matrix.
200
Identify where element 0 is.
A=[[4,-2,6],[-1,2,0],[3,5,-7]]
What is A23
200
***Triple Play***
2C + A
What is
|7 -19|
|0 15|
200
**Daily Double**
Find all three separate determinants:
[[-4,3],[-1,2]] , [[6,4],[-2,3]], and [[-8,-5],[3,0]]
-5, 26, and 15
200
Find the inverse of the following matrix:
[[3, 4],[-2, -1]]
[[-1/5, -4/5],[2/5, 3/5]]
300
Dimensions of a matrix m x n , m is the number of _________
What is rows
300
**Daily Double**
Do the following scalar multiplication and determine all elements of the result:
What is 4*(-4) 4*(3) 4*(-5)?
[[-16],[12],[-20]]
300
Can the following matrices be multiplied together? How do you know?
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.
300
Find the mistake in their steps to find the determinant, and then say what the correct answer should have been:
[[5,3],[-1,2]]
(5*2) + (3*-1)
(10) + (-3)
=7
They added the two products together instead of subtracting. The correct answer should be
10 - (-3) = 13
300
***Triple Play***
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.
400
**Daily Double**
What is the rule for determining if two matrices can be added or subtracted together?
What is the same order or dimension?
400
Do the following, and determine a13 of result:
What is a13 = 20?
[[-25,-30,20],[-20,10,5]]
400
Solve the following multiplication:
[[1,2, -2, -1],[-3, -4, 4, 3]] xx [[5],[6],[7],[8]]
[[-5],[13]]
400
Find the Determinant:
[[4,-2,6],[-1,2,0],[3,5,-7]]
What is -108
400
Find the inverse of matrix C. Identify element C12.
C=[(3,9),(3,2)]
[(-2/21,3/7),(1/7,-1/7)]
What is 3/7
500
The dimensions of the following matrix:
What are 4 x 2?
or
What are 4 rows by 2 columns
500
***Triple Play***
When multiplying the following matrices(A & B), what is the product at c32?
What is c32 = 1*3 + 6*4 = 27
500
**Daily Double**
Multiply
[[2,4],[-5,6]]*[[1,-4,0],[-1,-6,6]]
What is
[[-2,-32,24],[-11,-16,36]]
500
***Triple Play***
Find the determinant of matrix A and B. Then take the difference of the determinants matrix B and A (B-A).
A=[[-1,0,2],[0,1,2],[1,2,7]]
B=[[6,4],[-9,3]]
What is 59
Det(A)= -5
Det(B)= 54
54-(-5)=59
500
Find the inverse of matrix K and identify the smallest element.
K=[[3,2],[4,1]]
What is -3/5
[[-1/5,2/5],[4/5,-3/5]]