MCCC MAT203 Linear Algebra Prof. Porter's SAMPLE EXAM 2

- Use Gram-Schmidt process to generate an orthogonal set from the linearly independent vectors.
- Given the Function,
- Find the least-squares quadratic fit to the given data. Show the work, plot points and graph.
- Find the determinant of the matrix
- Given the matrix:
- Given the matrix:
- Given:

Normalize any two of the vectors above.

What would the set be called if all the vectors are normal?

Evaluate:

Determine if the function is a linear transformation.

For the given linear transformation, find the matrix A.

Describe the null space and range.

X |
1 |
2 |
3 |
4 |

Y |
3 |
2 |
3 |
5 |

Show how you would find the eigenvalues.

Give the characteristic polynomial.

Give the eigenvalues.

What is the algebraic multiplicity?

If x=2 Find the eigenvectors.

Is the matrix defective? Why?

Give the eigenvalues.

Give the eigenvectors

Determine if the matrix is diagonalizable.

If so, diagonalize it.

Calculate