Can you multiply Matrices?

To multiply matrices we have to:

1. We have to write a dimension statement to see whether or not the matrix can be multiplied.
2. If it can be multiplied then we multiply ROW x COLUMN.
3. Then get the sum of the product.

Dimension Statement Example:
[2   3] [-6]
[4   7] [-8]

Dimension Statement: 2 x 2 times 2 x 1

The numbers in green tell you whether or not the matrix can be multiplied, in this case they can be multiplied because the numbers are the same.
The numbers in blue tell you the size of the final answer.

Dimensions of a Matrix

• The matrix has 1 row and 3 columns. So the dimensions of this matrix is 1 x 3.

• 
  
   The matrix has 3 rows and 3 columns. So the dimension of this matrix is 3 x 3. Also called a Square matrix.

   





• The matrix has 3 rows and 2 columns. So the dimensions of this matrix is 3 x 2.

• The matrix has 3 rows and 3 columns. So the dimension of this matrix is 3 x 3. This matrix is an identity matrix. 

Error Analysis

The slope of this table should be 2, because the x values are increasing by 5. So the equation for this table would be y=2x+9.

The student only checked one equation to see if the solution is right. The student should check both equations. And the solution only solves 5x-y=7, not x+4y=-5.

For number 23, the line of the graph should be a dotted line instead of a solid line. For number 24, the graph should be shaded above the line instead of below because y is greater. 

The line on number 20 should be dotted instead of a solid line. The graph on number 21 should be shaded below because y is greater than or equal to.

Graphing Y=a|x-h|+k

When graphing y=a|x-h|+k, the a is an indicator of the slope of the graph. The h of the graph tells us whether we move the graph to the right or left. For example if the equation says x+h, then the graph moves to the left because it is opposite of the equation present. The k tells us whether the graph will move up or down. For example if the equation says plus k, then the graph will move up; therefore, h and k is the vertex of the graph.