MATH 3A Study Guide - Final Guide: Invertible Matrix, Diagonalizable Matrix, Linear Map

Determine if the columns of the matrix A = [-2 4 2 1 0 1 4 -4 0] are linearly independent A) Yes B) No Perform the matrix operation. Let A = [3 2 3 4] and B = [0 -1 4 6]. Find 4A + B. A) [12 7 7 10] B) [12 4 28 40] C) [12 1 16 10] Let A = [-1 2] and B = [1 0]. Find 3A + 4B. A) [1 6] B) [2 2] C) [-1 4]

Homework: Homework 4 Score: 0 of 3 pts X 1.4.19 Can each vectorin R be written as a linear combination of the columns of the matrix A? Do the columns of A span R4? Save 6 of 8 (8 complete) HW Score: 85%, 17 of 20 pts Question Help -2-2--2 0-4 2-12 2 05-8 Can each vector in R be written as a linear combination of the columns of the matrix A? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) 10 2.5-2 0 1-0.5 3 A. No, because the reduced row echelon form of Als 0 0 0-8 B. Yes, because the reduced row echelon form of A is

1. (8 pts) Evaluate the integral |(3x + 2y)2 /2y - x da over the region R bounded by A(0, 0), B(-2,3), C(2,5), D(4,2). Hint: Make sure the determinant is positive! OR xy 2. (8 pts) Evaluate the integral JR 1 + x2y2 z dA over the region R bounded by xy = 1, xy = 4, x = 1 and x = 4. Hint: Justify the choice x = u, y = v/u. 3. (6 pts each) Compute the following line integrals. (a) || (x2 + y2 + z)ds where C is the curve r(t) = (sint, cos t, t), Osts 37/4. dr where F(x, y) = (x + y,x - y) and C is the ellipse 4. (6 pts) Use the fundamental Theorem of Line Integrals to compute (, (2xy dx + (x2 + y2) dy where C is the curve y = x4 - x3, 0