Dimensions of a Matrix

-- The dimension of a matrix consist of the rows and columns that make it up.
          -Columns: vertical
          -Rows: horizontal

--When figuring out what the dimension of a matrix is you ALWAYS put the row first, then the columns.

This matrix has a dimension of 1x3 because it has one row(horizontal) and 3 columns(vertical)

This matrix has a dimension of 3x3 because it has 3 rows and 3 columns

This matrix has a dimension of 2x3 because it has 2 rows and 3 columns

This dimension is known as the Indentity Matrix (serves as the mulitplicative identity. This is also known as a 3x3 matrix since it has 3 rows and 3 columns.

Error Analysis

For this problem the x values are going up by 5 which would make the slope 2, not 10. After plotting the point on a graph the solution you get is not equal to y= 9 + 10x which is why this problem is wrong. The right equation would be y= 2x + 9.

mber 20 the line should be dotted because the y is only greater than the equation, not greater than or equal to. For number 21 it's wrong because the y is less than or equal to the equation which means it should be shaded below the line, not above.

For number 22 the y is only less than x +3 which would mean that it wouldn't be a solid line, but a dotted line and for number 23 the line is correct but the shading would need to be on the opposite side of the line since it's greater than, not less than.

After pluggin in the solution (1, -2) to both of these equations it shows that this solution works for the first equation but not the second one and in order for this point to be the correct solution in would have to work both of the problems.

Graphing y=a|x-h|+k

-The vertex of this equation in (h,k)

-a tells you whether the V opens up or down on the graph.

           -- you always go up and right then up and left, or down and right then down and left.

- the h determines whether the V moves right or left ( since it's the absolute values of h you use the opposite of that number)

-the k determines whether the V moves up or down.

Types of Systems

• Consistent/Independent: Has one solution (x,y), the lines intersect, and they have different slopes.

• Consistent/Dependent: Has infinite solutions with the same slope and the same y-intercept.

• Inconsistent: Has no solutions, the lines are parallel, and they have the same slope but different y-intercepts.