Linear algebra

Math_270_Final_Review_I.doc

Math 270 Final Review I

1. Find the eigenvalues and eigenspaces (as spans) for

2. Compute det

3. Compute the rank and nullity of

4. Find Col A and ker A (as spans) for A =

5. Solve the system of equations

x + y + z = 0

2x − 3y − z = 0

9x − 11y − 3z = 0

Write the solution space as a span.

6. Find the inverse of

7. Find a basis for the column space and the null space of

8. Write

as a linear combination of

and

9. Prove that S is a subspace if S=

10. Prove that if A is an nxn matrix with eigenvalue λ for eigenvector x, then 1/λ is an eigenvalue for

with eigenvector x.

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