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If you are finished with the kutaworks you can always go to khan academy and see if you have any assignments that you haven't done yet :)

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If you are finished with the kutaworks you can always go to khan academy and see if you have any assignments that you haven't done yet :)

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Please make sure you complete the kutaworks assignment on matrix multiplication before the zoom call

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Look at this guide to matrix multiplication and then complete the classwork assignment on kutaworks regarding matrix multiplication

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In the scalar variety, every entry is multiplied by a number, called a scalar. In the following example, the scalar value is $$ \blue 3 $$.

$ \blue 3 \begin{bmatrix} 5 & 2 & 11 \\ 9 & 4 & 14 \\ \end{bmatrix} = \begin{bmatrix} \blue 3 \cdot 5 & \blue 3 \cdot 2 & \blue 3 \cdot 11 \\ \blue 3 \cdot 9 & \blue 3 \cdot 4 & \blue 3 \cdot 14 \\ \end{bmatrix} \\ = \begin{bmatrix} 15 & 6 & 33 \\ 27 & 12 & 42 \\ \end{bmatrix} $

More on Scalar Multiplication

Multiply the matrix below by $$2$$

When can you multiply one matrix by another matrix?

You can multiply two matrices if, and only if, the number of columns in the first matrix equals the number of rows in the second matrix. (Link on columns vs rows )

In the picture above , the matrices can be multiplied since the number of columns in the 1st one, matrix A, equals the number of rows in the 2 nd, matrix B.

Two Matrices that can not be multiplied

Matrix A and B below cannot be multiplied together because the number of columns in A $$ \ne $$ the number of rows in B. In this case, the multiplication of these two matrices is not defined.

See 2nd Example

Another example of 2 matrices you can not multiply

Can the 2 matrices below be multiplied?

No

Since the number of columns in Matrix A does not equal the number of rows in Matrix B.

The multiplication of A and B is undefined.

So, what are the dimensions of the product matrix?

The product matrix's dimensions are (rows of first matrix) × (columns of the second matrix).

OK, so how do we multiply two matrices?

In order to multiply matrices,

Step 1: Make sure that the the number of columns in the 1st one equals the number of rows in the 2nd one. (The pre-requisite to be able to multiply)

Step 2: Multiply the elements of each row of the first matrix by the elements of each column in the second matrix.

Step 3: Add the products.

It's easier to understand these steps, if you go through interactive demonstrations below.

Matrix A and B below cannot be multiplied together because the number of columns in A $$ \ne $$ the number of rows in B. In this case, the multiplication of these two matrices is not defined.

See 2nd Example

Another example of 2 matrices you can not multiply

Can the 2 matrices below be multiplied?

No

Since the number of columns in Matrix A does not equal the number of rows in Matrix B.

The multiplication of A and B is undefined.

So, what are the dimensions of the product matrix?

The product matrix's dimensions are (rows of first matrix) × (columns of the second matrix).

OK, so how do we multiply two matrices?

In order to multiply matrices,

Step 1: Make sure that the the number of columns in the 1st one equals the number of rows in the 2nd one. (The pre-requisite to be able to multiply)

Step 2: Multiply the elements of each row of the first matrix by the elements of each column in the second matrix.

Step 3: Add the products.

It's easier to understand these steps, if you go through interactive demonstrations below.

Step By Step Demonstrations

Problem 1

Problem 2

Problem 3

Problem 1

Problem 2

Problem 3

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In the scalar variety, every entry is multiplied by a number, called a scalar. In the following example, the scalar value is $$ \blue 3 $$.

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Attendance.  Sign in here before 11:30 am!

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Attendance.  Sign in here before 11:30 am!