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

Find the determinant of matrix B.

 

Fill in the Blanks

Given the matrix, find the determinant.

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

Fill in the Blanks

Find the area of triangle ELI where E=(2, 11), L=(7, 1) and I=(2, 1)

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.

• 
  

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

• $$\left(-5,-2\right)$$

• $$\left(-3,-2\right)$$

• $$\left(5,1\right)$$