MATH 221 Midterm: MATH 221 2007 Winter Test 1 sec101

• School: UBC
• Department: Mathematics
• Course: MATH 221
• Professor: All

Document Summary

The rst 9 problems are common to all three sections, the last problem is section-speci c. Find a basis for the null space of the matrix. Your answer will depend on the value of t. Find a 2 2 matrix a such that. Problem 5. (6 points) (a) (4 points) find the determinant of the matrix. Problem 6. (6 points) (a) explain why b = {(cid:18)1 (b) find the coordinate vector of (cid:18) 7. 10(cid:19) in the basis b. (c) suppose the standard matrix of a linear transformation t : r2 r2 is. Find the matrix of t with respect to the basis b, i. e. , nd [t ]b. 5 (a) (2 points) verify that 1 is an eigenvalue of a. (b) (3 points) find all eigenvalues of a. (c) (3 points) for each eigenvalue, nd the dimension of the corresponding eigenspace. On a remote planet, moisture is present in clouds, on the continents, and in the seas.