For each pair of matrices A and B:
Is the product AB defined? If yes, answer part (ii).
Find the dimensions of AB.
A_{ 5 \times 4} and B_{ 3 \times 4}
A_{ 4 \times 2} and B_{ 2 \times 3}
A_{ 3 \times 2} and B_{ 5 \times 3}
A_{ 5 \times 3} and B_{ 3 \times 2}
Consider A=\begin{bmatrix} -7 & -3 & -1 \\ 5 & 7 & -6 \end{bmatrix}. If A is to be multiplied by B, a column matrix, find the dimensions of B.
If B is a 5 \times 2 matrix and the product AB is a 4 \times 2 matrix, find the dimensions of A.
A matrix calculation of A = BC resulted in A=\begin{bmatrix} -4 & -7 & 7 \\ -1 & 6 & 2 \\ 8 & -6 & 9 \end{bmatrix}. If B is a 3 \times 4 matrix, find the order of C.
The matrix A=\begin{bmatrix} -4 & 2 & 1 \\ -3 & -1 & 4 \\ 5 & 9 & 7 \end{bmatrix}is used in the matrix multiplication BAC. If the product BAC is a 3 \times 2 matrix, find the order of the following:
B
C
For each pair of matrices A and B:
Is the product AB defined? If yes, answer parts (ii) and (iii).
Find the dimensions of AB.
Find the matrix AB.
A=\begin{bmatrix} 5 \\ -1 \end{bmatrix}and B=\begin{bmatrix} -6 \\ 7 \end{bmatrix}
A=\begin{bmatrix} 7 \end{bmatrix}and B=\begin{bmatrix} 6 \end{bmatrix}
A=\begin{bmatrix} -4 & -7 \end{bmatrix}and B=\begin{bmatrix} 7 \\ -5 \end{bmatrix}
A=\begin{bmatrix} -3 & 7 & 8 \end{bmatrix} and B=\begin{bmatrix} -4 \\ 6 \\ -2 \end{bmatrix}
A=\begin{bmatrix} 9 & 1\\ 3 & -3\\ -8 & -6 \end{bmatrix}and B=\begin{bmatrix} -9 & 7\\ 5 & 2\\ 4 & -7 \end{bmatrix}
A=\begin{bmatrix} -9 \\ 3 \end{bmatrix} and B=\begin{bmatrix} 8 & 6 & -8\\ \end{bmatrix}
A=\begin{bmatrix} -8 & 3 \\ 4 & -4 \end{bmatrix} and B=\begin{bmatrix} 6 \\ -6 \end{bmatrix}
A=\begin{bmatrix} -1 & -3 \\ -9 & -4 \\ 4 & -5 \end{bmatrix} and B=\begin{bmatrix} 3 \\ -8 \end{bmatrix}
A=\begin{bmatrix} 6 & -1 & 4 \\ 8 & 9 & 7 \end{bmatrix}and B=\begin{bmatrix} -2 & 4 & 7 \\ 5 & 9 & 3 \end{bmatrix}
A=\begin{bmatrix} 9 & 2 & -5 \\ 7 & 5 & 6 \\ \end{bmatrix} and B=\begin{bmatrix} -2 \\ -1 \\ -9 \end{bmatrix}
For each pair of matrices A and B:
State the dimensions of AB.
Find the matrix AB.
A=\begin{bmatrix} -2 & -8 & 2 \\ 5 & -9 & 8 \\ 3 & 1 & 6 \end{bmatrix} and B=\begin{bmatrix} 7 \\ -1 \\ 4 \end{bmatrix}
A=\begin{bmatrix} -2 & 3 & 6 & -6 \\ 2 & -5 & -4 & 5 \\ \end{bmatrix} and B=\begin{bmatrix} -3 \\ 1 \\ -9 \\ 7 \end{bmatrix}
A=\begin{bmatrix} -3 & 1 \\ -4 & -7 \\ \end{bmatrix} and B=\begin{bmatrix} -8 & 6 \\ 2 & 7 \\ \end{bmatrix}
A=\begin{bmatrix} 5 & -1 \\ 3 & 9 \\ \end{bmatrix} and B=\begin{bmatrix} 8 & -5 & -3 \\ 0 & -8 & -9 \\ \end{bmatrix}
A=\begin{bmatrix} 4 & 1 \\ 7 & 5 \\ 2 & -6 \end{bmatrix} and B=\begin{bmatrix} -5 & 6 & -2 \\ -4 & 3 & 8 \\ \end{bmatrix}
A=\begin{bmatrix} -5 & 5 \\ 4 & 1 \\ -3 & 2 \\ 7 & -6 \end{bmatrix} and B=\begin{bmatrix} -4 & -2 & 8 \\ 6 & 3 & -1 \\ \end{bmatrix}
A=\begin{bmatrix} 9 & -5 & 8 \\ -4 & -3 & 6 \\ \end{bmatrix} and B=\begin{bmatrix} -6 & -9\\ 2 & 4\\ 5 & -2 \end{bmatrix}
A=\begin{bmatrix} 7 & 4 & -5 \\ -4 & 9 & 2 \\ -3 & 6 & 1 \end{bmatrix} and B=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}
A=\begin{bmatrix} 3 & 5 & 4 \\ -5 & 9 & -7 \\ -6 & -1 & 8 \end{bmatrix} and B=\begin{bmatrix} -8.3 & 7.4 \\ -3.4 & 1.5 \\ 6.1 & -1.7 \end{bmatrix}
A=\begin{bmatrix} 8 & -4 & -5 & 1 \\ 6 & 2 & -3 & 4 \\ 5 & 0 & -6 & 3 \end{bmatrix} and B=\begin{bmatrix} 8 & 5 \\ 7 & 6 \\ -1 & -2 \\ 4 & 3 \end{bmatrix}
Consider the following 2\times2 matrices:
A=\begin{bmatrix} 3 & 5 \\ 3 & 2 \end{bmatrix},\, B=\begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix}, \text{ and} \enspace C=\begin{bmatrix} 5 & 4 \\ 5 & 4 \end{bmatrix}
Find A \times B.
Find B \times C .
Find (A \times B) \times C .
Find A \times (B \times C).
Is (A \times B) \times C = A \times ( B \times C)?
Consider A=\begin{bmatrix} -5 & -6 & 0 \\ 3 & 2 & -8 \\ \end{bmatrix}and B=\begin{bmatrix} 5 & -2 \\ -7 & -1 \\ 8 & 9 \end{bmatrix}.
What are the dimensions of AB?
Determine the matrix AB.
What are the dimensions of BA?
Determine the matrix BA.
Is AB equal to BA?
Consider A=\begin{bmatrix} 2 & 7 \\ 3 & 8 \\ \end{bmatrix}and I=\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix}.
Determine the matrix AI.
Determine the matrix IA.
Is AI equal to IA?
Consider A=\begin{bmatrix} -5 & 9 \\ 4 & 2 \\ \end{bmatrix}and B=\begin{bmatrix} 0 & 1 \\ 1 & 0 \\ \end{bmatrix}.
Determine the matrix AB.
Determine the matrix BA.
Is AB equal to BA?
Find the matrix that satisfies the following equation:
\begin{bmatrix} 8 & 6 \\ 4 & 6 \end{bmatrix} \times \begin{bmatrix} ⬚ & ⬚ \\ ⬚ & ⬚ \end{bmatrix} = \begin{bmatrix} 8 & 6 \\ 4 & 6 \end{bmatrix}
Solve each of the following matrix equations for n:
\begin{bmatrix} -9 & -5 \\ \end{bmatrix} \begin{bmatrix} 5 \\ n \end{bmatrix} = \begin{bmatrix} -10 \end{bmatrix}
\begin{bmatrix} -3 & -4 & 5 \\ \end{bmatrix} \begin{bmatrix} n \\ 2 \\ -6 \end{bmatrix} = \begin{bmatrix} -14 \end{bmatrix}
\begin{bmatrix} 5 & -2 & 4 \\ -8 & -4 & n \end{bmatrix} \begin{bmatrix} -6 \\ 8 \\ -5 \end{bmatrix} = \begin{bmatrix} -66 \\ -14 \end{bmatrix}
A local bakery was selling three different products yesterday. The tables show the price that each product was sold for and the amount sold:
\enspace
Price:
| Meat pie | Croissant | Bread roll |
|---|---|---|
| \$5 | \$3 | \$4 |
\enspace
Quantity sold:
| Meat pie | Croissant | Bread roll |
|---|---|---|
| 22 | 13 | 35 |
Organise the prices of each product into the row matrix, A, in the order given in the table.
Organise the quantity sold of each product into the column matrix, B, in the order given in the table.
Calculate the bakery's total revenue for the day by finding AB.
In the last cricket season, the Darwin Darts had 14 wins, 1 tie, 6 draws and 8 losses.
The table shows the points system used in the competition:
Construct the team's results in each cricket match into a row matrix A.
Order the elements of A from left to right as the number of wins, ties, draws and losses.
Construct the points system into a column matrix B.
Order the elements of B from top to bottom as the points for each win, tie, draw and loss.
Find the matrix AB.
What does the matrix AB represent?
| Result | Points |
|---|---|
| \text{Win} | 6 |
| \text{Tie} | 3 |
| \text{Draw} | 1 |
| \text{Loss} | 0 |
Frank owns two pizza stores, Panania Pizza and Penrith Pizza, at which he sells small pizzas for \$7, medium-sized pizzas for \$15 and large pizzas for \$28.
The table shows the number of pizzas sold at each store on a particular day:
Organise the prices into the column matrix in ascending size order.
Organise the number of pizzas sold into the matrix as given in the table.
Calculate Frank's total revenue for each store using matrix multiplication.
| Small | Medium | Large | |
|---|---|---|---|
| Panania Pizza | 21 | 25 | 12 |
| Penrith Pizza | 26 | 11 | 22 |
Daniel's Dishes sells three different meals. The table below shows the number of items they bundle together into each type of meal:
| Hamburgers | Onion Rings | Chicken nuggets | Pizzas | Soft drinks | |
|---|---|---|---|---|---|
| Mega Meal | 5 | 5 | 10 | 4 | 4 |
| Hungry Meal | 2 | 8 | 5 | 3 | 3 |
| Crazy Meal | 1 | 9 | 12 | 0 | 0 |
Over the weekend the restaurant sold the following meals:
Saturday: 20 Mega Meals, 17 Hungry Meals and 16 Crazy Meals.
-
Sunday: 22 Mega Meals, 21 Hungry Meals and 25 Crazy Meals.
Organise the number of meals sold each day into a 2 \times 3 matrix A.
Organise the number of items in each meal into a 3 \times 5 matrix B as given in the table.
Find the matrix AB.
How many soft drinks did Daniel's Dishes sell on Saturday?
How many hamburgers did Daniel's Dishes sell on the weekend?
The quarterly mobile phone bills for three friends in 2019 are represented in the table below:
| Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 | |
|---|---|---|---|---|
| Sharon | 80 | 87 | 90 | 82 |
| Ray | 76 | 75 | 73 | 74 |
| Neil | 45 | 50 | 52 | 46 |