Q2) Let 21, 22, 23, 24, as be real numbers. Compute det ((a.) (1 :) ( ) ( ) ( .)) 1 1
Question 23 (1 point) Let o A = 3 1 Which of the following computes det(A) using the cofactor expansion along the third column? 2) 3 --) 1 +23 +2 이. o (3) 2 23 의
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73, 74, and has determinant det A = 1. Find the following determinants: ☺ U2 ü det 604 det det A +50 Note: You can earn partial creat on this problem Problem 1. (50 points) Let Rem -5 -20 -1 -1 - 1 4 16 0 الها (a) Compute dexA Use Cramer's rule to solve the following system 20x -5x -X -4 3 + 16x9...
Question 1. La 1 2] Let A = 6 3 4 Lc 5 6 for some a, b, c ER such that det A = 12. (a) (9 points) Determine the dimension of the column space of A. (Th mine the rank of A.) Justify your answer. (h) (8 points) Calculate the determinant of La-1 1 2] 6 - 2 3 4 - 3 5 6 (c) (8 points) Calculate the determinant of La 3 37 6 7 6 |...
5) Find the sum below, showing all steps and any formulas used. 1 2 22 23 214 4 4 4 (7 points) + ++ 4. 6) Solve the problem below using Cramer's Rule. Be sure to label what cach variable represents, show the equations in the system of equations, and show all matrices and determinants used. No other method will receive credit. Molly attended a coin auction and purchased some rare "Flowing Hair” fifty-cent pieces, and a number of very...
[i 1 -2] (a) Find det 2 3 5 by expansion along the 2nd row. (1 -1 3 (b) Use Cramer's rule to find the value of x in the solution to the system of linear equations shown below. (You may want to use your answer in part (a)). +y-2x = 0 2x + 3y + 5z = 3 2-y+32 = 0
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
(1 point) Let B= 1-3 -37 3 3 11 1] If possible, compute the following. If an answer does not exist, enter DNE. AC = help (matrices) BC = help (matrices)
(1 point) Compute the determinant of the matrix -1 -2 -4 -6 -7 -7 7 7 A= 0 0 0 0 -4 -5 7 det(A) (1 point) Find the determinant of the matrix 6 A- 6 -9 -7 det(A) (1 point) Find the determinant of the matrix 2 2 -2 B= 1 -1 2 3 -2 det (B)
2. [16 marks) - T (a) Evaluate the determinant of matrix A where: ſi 3 -1 0 2 -4 A= -2 -6 2 3 37 - 38 (b) Solve the following system of equations for 23 only, by using Cramer's Rule: [Again, your answer to part(a) may be helpful!] 21 +3.02 – 23 2x2 - 4.23 - 24 -221 - 602 +213 +324 3.01 + 7.02 – 3x3 +8.04 = 1 = 0 = -2 = 0 (c) Use your...