UCSF 137 Lecture 7: UCSF 137 - Lecture 7 (2)

9. Question Details SullivanCalc1 5.R.042. Find the integral. 、472 1 sin V x dx VX 2 å €

Determine whether b is in the column space of A. A = [1 1 -3 2 4 -2 -3 -6 5], b = [1 -2 -3] No Yes Find a basis for the null space of the matrix. A = [1 0 0 0 1 0 -7 5 0 -4 -2 0 {[7 -5 1 0], [4 2 0 1]} {[1 0 0], [0 1 0]} {[-7 5 1 0], [-4 -2 0 1]} {[1 0 -7 -4], [0 1 5 -2]}

Which of the following is the LU-factorization of the matrix [1 -4 0 1]? A) [1 0 -4 1][1 0 0 -1] B) [1 0 1/4 1][1 0 0 1] C) [1 -1/4 0 1][1 0 0 -1] D) [1 -4 0 1][1 0 0 1] E) [1 4 0 1][1 0 0 -1] The eigenvalues of the matrix [4 8 3 -1] are lambda_1 = -4 and lambda_2 = 7. Find an eigenvector corresponding to each of the given eigenvalues. Find the eigenvalues of the matrix [6 -9 -4 1] Use Cramer's Rule to solve the system of equations {8x-7y = 7 3x-y = 3. Find the area of the triangle having the vertices (-5, 3), (4, 6), and (-4, 6). Find the vector v for which v=u+6w given that u=(5, 7) and w=(-6, -5). Provided that u=(5, 4) and w=(2, -4), write v=(31, 8) as a linear combination of u and w, if possible.