Lesson 2 … and Row by Column Solidify Understanding

Ready

Add the given matrices. If the matrices can’t be added, give a reason why not.

1.

$[\begin{array}{rr} 5 & - 2 \\ 23 & 11 \end{array}] + [\begin{array}{rr} 10 & 8 \\ - 4 & 19 \end{array}]$

2.

$[\begin{array}{rr} 99 & 55 \\ 98 & 64 \\ 78 & 12 \end{array}] + [\begin{array}{rrr} 1 & 45 & 2 \\ 22 & 88 & 0 \end{array}]$

3.

$[\begin{array}{rrr} 70 & 14 & 62 \\ - 31 & 39 & 85 \\ 66 & 13 & - 7 \end{array}] + [\begin{array}{rrr} - 70 & - 14 & - 62 \\ 31 & - 39 & - 85 \\ - 66 & - 13 & 7 \end{array}]$

4.

$[\begin{array}{r} 6 \\ - 8 \\ 10 \end{array}] + [\begin{array}{r} - 10 \\ 8 \\ - 6 \end{array}]$

Set

5.

Recall from today’s lesson that in a context, each entry in a matrix represents two pieces of information, depending on the row and column in which it is located. Organize the following information into a matrix, and label the rows and columns.

The following number of items were sold during the lunch rush at Fried Freddy’s Café:

Day 1 – $65$ orders of fried chicken, $62$ orders of fish, and $145$ orders of french fries
Day 2 – $53$ orders of fried chicken, $60$ orders of fish, and $125$ orders of french fries
Day 3 – $76$ orders of fried chicken, $82$ orders of fish, and $198$ orders of french fries
Day 4 – $84$ orders of fried chicken, $68$ orders of fish, and $147$ orders of french fries
Day 5 – $91$ orders of fried chicken, $88$ orders of fish, and $203$ orders of french fries

6.

Find the product.

$[\begin{matrix} 1 & 1 & 2 \\ 2 & 2 & 3 \\ 1 & 3 & 4 \end{matrix}] \cdot [\begin{matrix} 15 \\ 5 \\ 10 \end{matrix}]$

7.

Find the product.

$[\begin{matrix} 10 & 20 & 20 \\ 20 & 14 & 5 \\ 11 & 15 & 2 \end{matrix}] \cdot [\begin{matrix} 5 \\ 2 \\ 8 \end{matrix}]$

8.

Find the product.

$[\begin{matrix} 4 & 3 & 0.5 \\ 2 & 1 & 3 \\ 5 & 4 & 0.25 \end{matrix}] \cdot [\begin{matrix} 25 \\ 30 \\ 20 \end{matrix}]$

9.

Find the product.

$[\begin{matrix} 5 & 2 & 4 \\ 4 & 4 & 4 \\ 8 & 2 & 5 \end{matrix}] \cdot [\begin{matrix} 9 \\ 15 \\ 25 \end{matrix}]$

Go

The following data represents a random sample of boys and girls and how many prefer cats or dogs. Use the information to answer the questions.

	Cats	Dogs	Total
Boys	$32$	$68$	$100$
Girls	$41$	$11$	$52$
Total	$73$	$79$	$152$

10.

$P (B) =$

11.

$P (G) =$

12.

$P (C) =$

13.

$P (D) =$

14.

$P (C | G) =$

15.

$P (C or B) =$

16.

$P (D | B) =$

17.

$P (B \cap D) =$

18.

If this is a random sample from a school, what total percent of boys in this school do you think would prefer dogs?

19.

What percent of students at the school would prefer cats?

20.

If you sampled a different 152 students, would you get the same percentages? Explain.

21.

What would happen to your percentages if you used a larger sample size?