MATH-0070 Final: MATH70 final Math70-FinalReview

• School: Tufts University
• Department: Mathematics
• Course: MATH-0070
• Professor: All

Document Summary

Math 46, review for final: (a) let a mm n, a = [aij]. De ne the following terms: cofactor of aij, det a, eigenvalue of a, eigenvector associated to an eigenvalue of a, eigenspace associated to eigenvalue of. A, a is diagonalizable. (b) for a function t : v v de ne the following terms: t is a linear transformation, t is diagonalizable. (c) describe the least squares method to solve ax = b. Ax = b? (d) what de nitions do you think will be on the test: let a mm n. Assume for all x rn that ax = 0. Prove that a is the zero matrix: solve the following linear system: 5x + 4y + 3z = 4 (a) by row reduction. (b) by cramer"s rule. [not covered in 2018: let a be an m n matrix and let ta : rn rm be de ned by ta(x) = ax.