Use Properties of Matrices

Matrix and Vector Operations Review

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Learning Target

Apply properties and operations to matrices and vectors

Matrice Operations

Think about the next two slides. This is what you must be able to do in order to master this standard.

Definitions

• Element

• Rows

• Columns

• Order

Adding and Subtracting

Order needs to be the same

Add (or subtract) corresponding elements

Multiple Choice

In Matrix R (pictured) what is the value of element R_3,2

• 8
• 9.01
• 6
• 1

Multiple Choice

What is the value of element a₂₃?

• 2
• -1
• 6
• 1

Multiple Choice

Find B-A

• -3     1
  7     -1
• 1     0
  1     -4
• 4       0
  -6     0
• not possible because rows do not match columns

Multiple Choice

Find A+B

• 8     10
  8      1 
• 12     25
  7     1
• 10     30
  0     1
• can't add two together because the rows dont match columns

Multiple Choice

Subtract

• 3    -8
  0   -1
• 3   -4
  8  -13
• -3   8
  0    1
• 3   -8
  -8    1

Multiple Choice

What are the dimensions of this matrix?

• 2 x 3
• 3 x 2
• 6 x 1
• 1 x 6

Multiple Choice

Add

• 11    8
  -4     2
• 3     2
  -6    -6
• -3    2
  -4    -6
• 10    8
  -6    2

Multiple Choice

What must be true in order to ADD two matrices?

• They must be square.
• The dimensions must be equal.
• The determinant can't equal 0.
• The column of the 1st must equal the row of the 2nd.

Multiple Choice

In Matrix R (pictured) what element is in the second row, third column?

• 8
• 9.01
• 6
• 1

Multiple Choice

Subtract

• -5
  -8
  3
  10
• -9
  8
  3
  2
• 5
  -8
  3
  10
• -5
  8
  3
  2

Scalar Multiplication Matrices

It is like distribution

Multiple Choice

What do m, n, p and q equal in this scalar matrix multiplication?

• m=8, n=9, p=-4, q=4 
• m=15, n = -45, p=20, q=-5
• m=20, n=-5, p=15, q=-45
• m=-5, n=20, p=-45, q=15

Multiple Choice

Multiply

• 20     15    -10
  30     -5         0
• -20      15     -10
  30     -5          0
• 1        8       3
  11     4        5
• 20     -15     10
  -30         5        0  

Matrix Multiplication

Check to see if the two matrices are compatible to multiply

Number of columns in the first matrix= number of rows in the second matrix

Matrix Multiplicaiton

• Step 1: Check compatibility

• Step 2: multiply the first row in the first matrix by the first column in the second matrix (multiplying the first numbers and adding them to the product of the second numbers)

• Step 3: Multiply the first row of the first matrix to the second column in the second matrix

Matrix multiplication

• Step 4: repeat until you have multiplied the first row of the first matrix to all of the columns in the second matrix

• Step 5: do the same with the remaining rows of the first matrix

• Step 6: Simplify

Multiple Choice

You can multiply a 2X3 matrix by which matrix?

• 2X2
• 2X12
• 3X12
• 2X3

Multiple Choice

Find the product.

• undefined
• -3   16
  17   12
  8   -10
• 3   12 
  -15  -8
  -1   -3

Vectors- definitions

• Components

• 
  

• 
  

Vector Mastery

what you need to be able to do to master this standard

Adding and Subtracting Vectors

• Add or subtract corresponding parts

• Simplify

Scalar Multiplication

• "ditribute" the scalar to all parts of the matrix

• Simplify

Multiple Choice

Given u = <3, 7> and v =<-5, 4>, find 2u - 3v

• <21, 2>
• <-11, 26>
• <8, 3>
• 23

Multiple Choice

If w = <2, -5> and y = <2, 0>, find 2w + y.

• <-10, 2>
• <4, -5>
• <-6, 10>
• <6, -10>

Multiple Choice

If v =〈a,b〉, then a is the ___________ component of v.

• vertical
• horizontal
• parallel
• slope

Multiple Choice

If c=<-5, 4> and d=<8, 0>, calculate 2c+d

• <-2, 8>
• <-2, 0>
• <6, 8>
• <6, 0>

Learning Logs

Time to reflect on learning.