Identifying Quadratic Functions

The standard form of a quadratic function is  ax² + bx + cy² + dy + e= 0.

The function 4x²+4y²=36 is a circle because a=c (or the coefficients for a are equal to those to c).

The function 2x²+4y²=3 is an ellipse because a does not equal c.

If a or c equal zero, then the equation is a parabola, like 3x+5y²=6.

The function 7x-8y=4 is a hyperbola because a and c are different signs.

Multipying Matrices

Scalar multiplication is when you distribute the number outside the matrix to all the numbers inside the brackets.

To multiply matrices, you first need to write a dimension statement. The dimension statement basically states that the columns of the first matrix must match the rows of the other matrix
For example:

     2 x 2              2 x 2                                                                   

             

     

                                                                  

         2 x 2   times    2 x 2 

The numbers highlighted show that the matrices can be multiplied, since the inside numbers are the same.

  2 x 2   times    2 x 2

These numbers become the dimensions for the product matrix.

After you determined that the matrices can be multiplied, then you start to multiply them together. To do this, you would multiply the first row of the first matrix with the column of the second matrix. More specifically, you would multiply the first number of the first row  on the first matrix with the first number of the first column of the second matrix. You then add the products together and thats the first number of the product matrix. You repeat this until all the numbers of both the matrices have been multiplied, giving you your product matrix.