Math 2568: Midterm #1

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Math 2568: Midterm #1

1. Solve the system of equations.

2. Solve the system by transforming the augmented matrix to reduced echelon form using the elemen tary row operations. Write the general solution.

3. Represent the general solution of the system

from Problem 2 in vector form.

4. For what value of a does the system

have nontrivial solutions?

5. Perform the multiplication of matrices

6. Express a vector as a linear combination of and

7. Determine whether the set of vectors

is linearly independent or linearly dependent? If the set is linearly dependent, express one vector as a liner combination of others.

8. Find the value of a for which the vectors

are linearly dependent.

9. Find the inverse A−1 of the matrix

10. Using the answer to Problem 9 find a solution of the system