Dimensions of a Matrix

In a matrix, it is organized ROW x COLUMN. Row are horizontal and columns are vertical.

 

 This matrix is 1x 3 because there is 1 row and 3 columns.

 This matrix is 3 x 3 because there is 3 rows and 3 columns.

 This matrix is 3 x 2 because there is 3 rows and 2 columns.

This matrix is 3 x 3 because there is 3 rows and 3 columns.

Errors !

The equation is actually y=2x+9. You can figure this out simply by plugging in a (x,y) represented in the table and it would not work. The slope is not 10 because the y's go up by 10 and the x's go up by 5. Thinking of rise over run, 10/5 is reduced to 2.

The student did not plug the coordinate into the second equation. When you plug it into the second it does not work so it is not a solution.

The problem in this is that the first graph's line is suppose to be dotted. The second graph is suppose to be shaded above.

The slope line on number 20 should be dotted and on number 21 should be shaded below.

How to graph absolute functions

The parent function is y=a|x-h|+k. The vertex is (h,k). So if the function was y=|x-9|+1, then the vertex would be (9,1) But if inside the absolute value sign it said 'x+9' then the vertex would be (-9,1). The 'h' controls the shift from left or right on the graph. The 'a' controls if the 'V' shape it the function makes is open up or down and the slope (vertical stretch or horizontal shrink). The 'k' controls the up or down postion of the function. So if you wanted to graph y=|x|+2 it would look like this..

And if you wanted to graph y=|x-3| it would look like this...

System of Equations

Consistent Independent- The two lines intersect at one point (x,y). One solution.












Inconsistent Dependent- The two lines have the same slop but different y-intercepts and they never cross. No solutions.

Consistent Dependent - The two lines have the same slope and y-intercept. All solutions.