We proceed the same way to obtain the second row of
In other words, row 2 of
times column 1 of
row 2 of
times column 2 of
row 2 of
times column 3 of
When complete, the product matrix will be
Properties of matrix multiplication
For the matrices
and
the following properties hold.
Matrix multiplication is associative:
Matrix multiplication is distributive:
Note that matrix multiplication is not commutative.
Multiplying two matrices
Multiply matrix
and matrix
First, we check the dimensions of the matrices. Matrix
has dimensions
and matrix
has dimensions
The inner dimensions are the same so we can perform the multiplication. The product will have the dimensions
As the dimensions of
are
and the dimensions of
are
these matrices can be multiplied together because the number of columns in
matches the number of rows in
The resulting product will be a
matrix, the number of rows in
by the number of columns in
The dimensions of
are
and the dimensions of
are
The inner dimensions match so the product is defined and will be a
matrix.
Yes, consider a matrix A with dimension
and matrix B with dimension
For the product AB the inner dimensions are 4 and the product is defined, but for the product BA the inner dimensions are 2 and 3 so the product is undefined.
Using matrices in real-world problems
Let’s return to the problem presented at the opening of this section. We have
[link] , representing the equipment needs of two soccer teams.
Wildcats
Mud Cats
Goals
6
10
Balls
30
24
Jerseys
14
20
We are also given the prices of the equipment, as shown in
[link] .
Goal
$300
Ball
$10
Jersey
$30
We will convert the data to matrices. Thus, the equipment need matrix is written as
The cost matrix is written as
We perform matrix multiplication to obtain costs for the equipment.
The total cost for equipment for the Wildcats is $2,520, and the total cost for equipment for the Mud Cats is $3,840.
Given a matrix operation, evaluate using a calculator.
Save each matrix as a matrix variable
Enter the operation into the calculator, calling up each matrix variable as needed.
If the operation is defined, the calculator will present the solution matrix; if the operation is undefined, it will display an error message.
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?