Multiplying Matrices

Scalar matrix multiplications
Distribute the outside number for all the numbers on the inside.

When multiplying matrices. We must note that the dimensions are to be similar. The colums of the 1st matrix and the rows of the 2nd matrix must be equal. Then use the outer dimensions as the product matrix. So...
If we multiply a 2×3 matrix with a 3×1 matrix, the product matrix is 2×1

Here is how we get M₁₁ and M₂₂ in the product.

M₁₁ = r₁₁× t₁₁  +  r₁₂× t₂₁  +   r₁₃×t₃₁
M₁₂

 

 

Dimensions of a matrix

When identifying the dimensions of a matrix. One must always follow the rule. Row Times column.
For example if there are 4 rows and 5 columns. The dimensions of the matrix would be.
4 X 5.

Ex: There are 2 rows and 4 columns. Therefore the dimensions of the matrix would be 2 x 4.

*Be carefull that you don't go columns by rows. Many people mess up like this.

The rule is : Rows x Columns

Error Analysis - Systems of Equations + How to graph equations.

Many times while doing systems of equations people have common errors in their calculation.

Example :
Equation : Y= 2x+4
Y= 5x-1

Many people make this mistake. When graphing we must consider three things of the Y= MX+B equation.
B is the vertical shift in which we shift the parent graph to our equation. If B were 4 we are to shift up 4. In which the person doing this graph only shifted up 3. That is the mistake. To completely graph the equation Y=2x + 4. First we must go up 4 on the y axis. Then due to the slope being 2. We must follow the slope rule, Rise over run, Therefore we go up 2 and over 1.

And for the second equation the same rule applies.  Y= 5X-1. The graph would shift down one. Then it would strech due to the slope being 5/1. Remember that slope is rise over run. Therefore you go up 5 and over one to get your second point after shifting down 1.