Reference no: EM131076175
MIDTERM 1-
Problem 1- Consider the matrix
Find rank A, a basis for Col A and a basis for Row A
Problem 2- Compute (or if undefined say so, explaining why)
Problem 3- (a) State Cramer's Rule.
(b) Use it to solve the linear system (no credit for solving the system directly)
Problem 4- Mark each statement True or False. Justify your answers.
(a) If AB = 0 for two square matrices A, B, then either A = 0 or B = 0.
(b) The set P2[X, Y] of all polynomials in X and Y of degree at most 2 (together with the usual addition and multiplication by a constant) is a vector space of dimension 6.
Problem 5- Let P4 denote the vector space of polynomial of degree at most 4 (vector space together with the addition and multiplication by a constant). Consider the differentiation map D : P4 → P4 given by Df = f'.
(a) Show that D is linear.
Problem 6- Mark each statement True or False. Justify your answers.
(a) If there is a linear transformation T : R5 → V which is onto, then dim V ≥ 5.
(b) Any linearly independent set in R3 must have exactly three elements.
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State cramer rule
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