Exit Exam Sample Questions for Matrix Algebra

• Gaussian elimination to solve linear systems

1) Using Gaussian elimination, one nts/solving-nonlinear-systems-with.html">solve the system



2) Give the general solution ( in variables ) for the system having the augmented
matrix



• Basic matrix operations

Suppose and . Either calculate each of the
fol lowing or explain why the calculation cannot be done.

a)

b) 

c) 

d) 

e) 

• De terminants up to 4x4

Calculate the determinant



• Eigen values and eigenvectors

1) For.

a) Find the eigenvalues of A.

b) Find an eigenvector corresponding to each eigenvalue of A.

2) Find the eigenvalues of .

• Standard vector spaces , and

1) Give the dimension of .

2) Describe the vectors in the vector space .

3) Give the standard basis for the vector space .

• Linear dependence /independence  in or

1) Is the set of vectors   in linearly independent or linearly
dependent? Justify your answer.

2) Is the set of vectors   in linearly independent or linearly
dependent? Justify your answer.

• Subspaces
1) Is the subset of a subspace of ? Justify your answer.

2) Is the subset of a subspace of ? Justify your answer.

• Linear transformations

1) Is the function   given by a linear transformation?
Justify your answer.
2) Suppose   is a linear transformation with and
Find .