multipling Matrices

Dimensions statement:
2 X 2 times 2 X 1

These matrices can be multiplied, so you would multiply row X column.
Then you get the sum of the products.
The numbers in yellow tell you that you can multiply the matrices.
The numbers in red tell you the size of the final matrix. 

 

describe graphing

x

 




 Y=a abs(x-h)+k

• When ever you have these types of graphes the general shape will look like a “v” or it will be upside down indicating a negative is in the a part of the equation . 
•  
• You find the vertex by the H and the K in the equation , one key thing to remeber is that the H is always the opposite to the equation . 
•  After finding the vertex them you can graph   

types of systems

 Consistent-Independent. One solution. Lines that have different slopes.

Consistent- Dependent. All numbers/infinite.Lines that have the same slope, and same y-intercepts.

Inconsistent-No solutions and parallel. Lines that have the same slope, but different y-intercepts.

Dimensions of a Matrix

This dimension is called an Identity Matrix.   It serves as the multiplicative identity. 

The numbers of rows and columns are the dimensions.The dimensions of a matrix refer to the number of rows and columns.The rows are the numbers going horizontal.The columns are the numbers vertical.When stating the dimension, the correct form would be the number of rows multiplied by the number of columns.

This matrix is one row by three columns or 1 x 3 matrix.

    This matrix is three rows by three columns or 3 x 3 matrix.

This matrix is three rows by two columns, so it is a 3 x 2 matrix.

Error analysis

In this problem the value of x is going up by 5 so the slope should be 10/5. y is also not equal to 9+10x in the chart. they need to finish sloving the equation.

error analysis

For the students work to be able to be write it has to solve both equations but it only solved the first one and not the second one so it is not a solution of the system.

error analysis

 

In problem number 20 the line should be dotted because there isnt a line under the greather than sign.
In problem number 21 the shading is wrong, it should be shadeed below because the sign is less than.

error analysis

In problem 22 the thing they did wrong was they didn't make the line dashed. It needs to be a dashed line because its not equaled to there needs to be a line under neath for it to be solid.
In problem 23 the thing thats wrong is that they didnt shade above the solid line. It needs to be shaded above because the sign is greater than.