Exam 3 Practice Problems - Calculus II | MATH 1502, Exams of Calculus

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Practice Test 3H for Math 1502 I.(a) Let f be the transformation of R? to R? defined by x z-y f y =|r-z z y-2 1s this transformation linear? If so, write down the corresponding 3 x 3 matrix. If not. explain why not. (b) Let g be the transormation of R to R° defined by xo RY gl 9] ] =| az z yt Is this transformation linear? If so, write down the corresponding 3 x 3 matrix. If not, explain why not. 1 12 -2 1 II. Let A be the matrix A = 21 2), and letv = / 2]. —2 2 1 2 (a) Compute |v] and {Av}. (b) Compute the angle between v and Av. Leave your answer in terms of an inverse trigonometric function; do not give the decimal value. (IIL) Consider the system of equations e+ Qyt2=-1 3a —y+2z=2 2e+ytaz=b (a) For which values of a and &, if any, does this system have a unique solution? (b) For which values of @ and d, if any, does this system have no solution? (c) For which values of a and 5, if any, does this system have infinitely many solutions? Continues on next page