Dimensions of a Matrix

The dimensions of a matrix refer to the number of rows and number columns of a given matrix.

The rows of a matrix are the numbers going horizontally.

The columns of a matrix are the numbers going vertically.

To find the dimensions of a matrix you must multiply the (number of rows x the number of columns). The dimensions for the matrix above would be (2 rows x 3 columns). The dimension of the matrix is 2 by 3 or (2x3).

Error Analysis

In the table the inputs or x-values increase by 5 ,meaning the slope has to be different. A equation that represents the table is y = 2x + 9.

The student checked the shown equation wrong because they didn't plug the solution in to the other equation. When you plug in (1,-2) in to x + 4y = -5 you get 1-8=5 which is -7 = 5 meaning no solution.

22. The inequality y < x + 3 is graphed incorrectly because the line should have a dashed line instead of a bold straight line. When an equation has a < or > sign and it doesn't have a line underneth them you must graph the line as a dashed line through the points that make up the slope of the equation.

23. The inequality y > -3x - 4 is graphed incorreclt because the inequality should be shaded above the line instead of below the line. When you have y > an equality you must shade above the graph to show that the y-intercept  is greater than the inequality.

For #20, the line should be dashed because it is >. In #21, the shaded area should be


below the absolute value line because y <.

Graphing y = a|x-h|+k

In the equation Y= /x-h/ + k, there are many ways in which the absolute value graph can be altered.

• 
  
  The symbolsHand K make up the vertex
• The H value inside the absolute value sign directs the point left/right, while the K on the outside directs the point up/down. 
• If the H value is positive, the point should be shifted to the left. If negative, it should go the the right. The movement of the H value always goes opposite, while the K value goes up/down the normal way.
• If there is a negative value before the absolute value sign, the graph should open down. If positive, the graph should open up.

Systems of Equations

Consistent Independent - Has 1 solution. Two different equations with different slopes. Lines cross at one point. Only Solution is where the lines cross. Does not pass the vertical line test.

Consistent Dependent - Has infinite solutions. Has many lines with the same slope and same y-intercept and the lines overlap themselves, therefore it is the same line.

Inconsistent - Has no solution. Has two or more lines with the same slope but different y-intercepts. This system of equations does not pass the vertical line test.