Dimensions of A Matrix

Matrices are identified Row X Column

The Matrix above is 3x3.

Count the rows and columns, show how to identify the dimensions

1 x 3

3 x 2

3 x 3

Error Analysis Examples:

X. In number 22, the line should not be solid, but dotted because

it is not "equal to" the given equation.

X. The shading in the line is wrong because it should be shaded

above the line, instead of below it.

X. This analysis is wrong because the given solution does not work

in the second equation. To find the solution, the student should use substitution

or elimination to figure out the solution.

X. This problem is wrong because if you use the given equation, y=9+10x, it does not match with the table above. To find the right equation, graph the table given and find the slope, then write an equation. The answer is:  y = 2x + 9.

X. Number 20 is wrong because the line is supposed to be dotted because it is no equal to the given equation.

X. Number 21 is supposed to be shaded below the given line because it is y is lesser than or equal to the given equation, not greater than.

Graphing y=A|x-h|+k

(h,k) of the equation y=A|x-h|+k is the vertex.

'h' moves the graph on the x intercept while 'k' moves it on the y intercept.
h = horizontal movement , y = vertical movement

Example:

Types Of Systems

01.  Inconsistent Systems has no solutions and never intersect. They are parallel. (same slope, different y-int)

02. Consistent & Independent Systems have one solution and they intersect.

03. Consistent & Dependent Systems have an infinite amount of solutions and they are the same line (same slope & y-int)