11B Review

Multiple Choice

A ______ is a rectangular array of numbers symbols, or expressions

• matrix

• element

• rows

• columns

Multiple Choice

$$𝑀=[4]$$  

• 1 × 1 matrix

• 1 × 3 matrix

• 3 × 1 matrix

• 3 × 2 matrix

​A farmer had some chickens and some cows. She counted 40 heads and 126 legs. How many chickens and how many cows did she have?

​At a school fundraiser, there were two types of food items for sale: hamburgers and hot dogs. The total number of items sold was 150, and the total revenue was $450. Hamburgers were sold for $3 each, and hot dogs were sold for $2 each. If H represents the number of hamburgers sold, and D represents the number of hot dogs sold, how many of each were sold?


Maria has some quarters (25 cents) and dimes (10 cents) in her piggy bank. She counts a total of 12 coins, and the total value is $1.65. How many quarters and dimes does Maria have?

Multiple Choice

What is a Matrix?

• An equation of over 5 numbers or symbols 
• A set of numbers in rows and columns
• A method of finding the n^th value of a series
• A complicated number system

Multiple Choice

What is the name of each entry of a matrix?

• Row
• Element
• Dimension
• Rectangle

Multiple Choice

What is the value of element a₂₃?

• 2
• -1
• 6
• 1

Multiple Choice

How many columns are in a 5 x 4 matrix?

• 5
• 4
• 20
• 9

Multiple Choice

What are the dimensions of this matrix?

• 2 x 3
• 3 x 2
• 6 x 1
• 1 x 6

Multiple Choice

Dimensions?

• a
• b
• c
• d

Multiple Choice

Matrices A and B are equal, Find the value of

x and y.

• x=4

  y=7

• x=0

  y=4

• x=7

  y=4

• none

Multiple Choice

Find AB=

• none

Fill in the Blanks

Fill in the Blanks

Multiple Choice

Find the determinant of the matrix and determine of the matrix is invertible.

• det = -14, inverse exists

• det = 0, no inverse exists

• det = 166, inverse exists

• det = 14, inverse exists

Solving for an unknown:

• det A = ad - bc

• -3x - 5 = 16

• -3x = 21

• x = -7

Determinants:

Area of a Triangle

• Area of Triangle is 1/2(bh). Given the vertices in the coordinate plane...

• x-coordinates in 1st column

• y-coordinates in 2nd column

• all 1's in 3rd column

• Find det of 3x3

• Area should always be positive, so multiply by 1/2 accordingly

Example: Find the area of a triangle whose vertices have the coordinates

(1, 2), (4, 0), and (6, 2)

see the next slide

Multiple Choice

A triangle has vertices as (1, 2), (3, –4), and (–2, 3). Find the area of the triangle.

• Area = 16

• Area = 8

• Area = 32

• None of these

Adding and subtracting Matrices

Identity Matrix

Scalar Multiplication

Multiplication

In general, the product of a 'm x n' matrix A with a 'n x p' matrix B is the 'm x p' matrix AB. The number of columns has to be equal to the amount of rows for the multiplication to occur. For instance :

• 1 x 2 by a 2 x 3 gives a 1 x 3

• 1 x 2 by a 2 x 1 gives a 1 x 1​

• 2 x 1 by a 1 x 2 gives a 2 x 2 ​

• ​2 x 2 by a 2 x 2 gives a 2 x 2

Examples

Equal Matrices

Determinant of a 2 by 2 matrix.

Inverse of a non-singular 2 x 2 matrix.

Matrices and simultaneous equations.

Steps :

1. Put the equations in matrix form. (AX = B)

2. ​Determine the inverse of the coefficient Matrix. (A^-1)

3. Make matrix X , with unknown values, the subject​. ( X = A^-1 B)

4. Solve for unknown constants.​ (Multiply the 2 matrices and equate corresponding values)

Multiple Choice

Can the operation be performed?

• Yes
• No
• Sometimes
• only Mrs. Jordan knows

Multiple Choice

image

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  

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

• 1   2
  6   -8
• -3   -5
  -5   -11
• -2     8
  -6   -12
• 2  -3
  5   -2

Multiple Choice

You can multiply a 2X3 matrix by which matrix?

• 2X2
• 2X12
• 3X12
• 2X3

Multiple Choice

These matrices are being multiplied. Determine the dimension/size of the new matrix. 

• Can't multiply them
• 4  x  2
• 3  x  3
• 4  x  3

Multiple Choice

Calculate the determinant

• 0
• -15
• -70
• 10

Multiple Choice

What is the inverse of this matrix?

• _{(1/25)  (-4/25)
  (3/25)  (13/25)}
• _{(1/5)  (-4/5)
  (3/5)  (13/5)}
• _{(6/25)  (-2/25)
  (2/25)  (9/25)}
• _{(1/150)  (-4/150)
  (3/150)  (13/150)}

Multiple Choice

Solve for the determinant of the following matrix:  
⌈12  −3⌉
⌊−6  15⌋
*detA= ad-bc

• 198
• 162
• -333
• -9

Multiple Choice

Solve the system of equations using Cramer's Rule.

• 
  

  $$\left(6,-6\right)$$
  

• $$\left(-6,6\right)$$

• $$\left(-6,2\right)$$

• $$\left(2,-6\right)$$

Multiple Choice

Solve the system of equations using Cramer's Rule.

2x + y = 7

x + 4y = 7

• (1, 3)

• (3, 1)

• (3, -1)

• (-1, 3)

Multiple Choice

Solve the system of equations using Cramer's Rule.

• 
  

  $$\left(-4,0\right)$$
  

• $$\left(-5,-2\right)$$

• $$\left(-3,-2\right)$$

• $$\left(5,1\right)$$