11.4 Matrix Algebra

11.4 Matrix Algebra

Order matters when multiplying

Multiple Choice

A little review first...which of these is a 3x4 matrix?

Multiple Choice

Which of these is Reduced Row Echelon Form for a matrix?

Multiple Choice

Which of these has a solution to the system that is considered inconsistent.

Multiple Choice

Which of these has a solution to the system that is consistent and dependent

11.3 Matrix Algebra

• Add and subtract matrices

• Multiply a matrix by a scalar

• Find the product of 2 matrices

• Determine the inverse of a matrix

• Use inverse to solve a system

Add/Subtract

Matrix dimensions MUST match

First matrix is 2x2 and the second matrix is 2x2. Simply add the values in the corresponding cells

Matrix A and Matrix B have the same dimensions so let's add them...

• Notice that matrices are labeled with a capital letter.

• Answer provided on next slide

Multiple Choice

Now A-B

Don't over think this! Visually take the + sign out between the 2 matrices and replace it with a - sign. Do this now and choose an answer on the next slide. : )

Multiple Choice

A-B=

Multiple Choice

Which below are A-B

These cannot be added.

• Do you know why?

• Answer on the next slide.

Multiple Choice

Why could we not add the matrices on the previous slide.

• the dimensions do not match.

• the matrices are not equal

• the first entry is negative and you cannot add with a negative value.

• the second matrix had too many zeros

Here is an example of 2 equal matrices

of course one has values that need to be simplified.

scalar multiple looks like this

• A matrix

• 3A which means multiply all elements in matrix A by 3.

If this is matrix B determine...

• -2B

Multiple Choice

-2B would be which matrix below?

Time for...

• dimensions MUST match to add or subtract matrics

• a scalar multiple effects EVERY element in a matrix

• equal matrices have the same dimensions and EXACTLY the same values for each element.

Multiplying a matrix by another matrix

things get a bit more challenging here.

We showed you the "why" you multiply the way we do.

Here comes the next step

Multiple Select

Which matrix can be multiplied with matrix A in this order A(?) if matrix A is a 3X4 matrix. Check all that apply

• 4X1

• 3X4

• 4X3

• 4X4

• 2X4

Multiple Choice

Determine the new matrix of CB (order matters in multiplying matrices) BE CARFUL HERE!!

Obtaining the inverse of a matrix is challenging

Need to use RREF and Identity matrix. Video coming up!

That's a lot of work

Next is how you use the inverse matrix

Try using

 $A^{-1}$  matrix to get a solution.

• The system of equations is to the right.

• A and A inverse are also there.  Use these to find the solutions to this system.

Multiple Choice

the solution as an ordered pair is...

• (-8, -15)

• (-5, 24)

• (15,8)

• Don't pick this one BUT, thank goodness the inverse was provided.

Shortcut 2x2

Using variables to understand

Go Practice!