Answer to Question #307856 in Linear Algebra for Simons

Question

How to show the polynomials are linearly dependent or independent

How to determine the radius and coordinates of a circle while given equation

Using the row reduction method to solve equations

Answer 1

a). It can be done using the Gauss elimination and totaling non-zero rows and associating this number to the number of polynomials. Alternatively, if one has a matrix where columns are the coefficients of the polynomials then take them. The system is linearly independent if the determinant is non-zero.

b). The formula for the equation of a circle is (x – h)²+ (y – k)² = r², where (h, k) means the coordinates of the center of the circle, and r means the radius of the circle.

c). 1. Multiply a row by a non-zero constant.

2.   Add one row to another.

3.   Exchange rows.

4.   Add a multiple of one row to another.

5.   Write the augmented matrix of the system.

6.   Row reduces the augmented matrix.

7.   Consider the new, equivalent, system that is well-defined by the new, row condensed matrix.