Find the determinant of the following matrix as a formula in terms of x and y....
1 2 2 1 -X Find the determinant of the matrix as a formula in terms of x and y. Remember to use the correct syntax for a formula 0 0 1 -3 -x X Question 4: (2 points) a b c fis 3, find the determinant of these matrices: If the determinant of the matrix M = d e (gh k) b a C (a) 7 d 7e 7f h k -E. b-2 e c - 2 f a...
find A^-1 using the matrix of coefficient and determinant method 5, x+y+ z= 5 x+y-4z = 10 -4x + y + z= 0
Dºx-4Dy = 667 1. Consider . Use the determinant of the coefficient matrix (D+2)x+(D+2) y = 81 to solve for x. (Find both x, and x,. Do not solve for y.) (15 pts).
1. Use the cofactor expansion formula to calculate the determinant of the following matrix. 1-2 5 2 0 0 0 2 -6 -7 5 5 0 4 4 درا
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...
Use expansion by cofactors to find the determinant of the matrix. - 3 4 -1 13 1 2 | -1 4 2 Use expansion by cofactors to find the determinant of the matrix. [65 31 0 4 1 00-3]
Compute the determinant of the following n x n matrix: [ 2-1 -1 2-1 -1 2 2 -1 -1 2 (All "missing" entries are 0.) This is a nice exercise in mathematical induction. To do this problem, first try computing a few specific cases, then make a conjecture about the general nxn determinant. Then prove that your conjecture is correct by induction. (Actually, you will use strong induction, where you assume that the determinant in the nxn case follows from...
Use the fact that cA| = |A to evaluate the determinant of the nxn matrix. A= - [1 12 15 3 -9 STEP 1: Factor out the greatest common divisor. 12 15 3 -9 = STEP 2: Find the determinant of the matrix found in Step 1. STEP 3: Find the determinant of the original matrix.
Question 19 [10 points] If the determinant of the first matrix below is as given, find the determinant of the other matrix. a b c det r s t 5 x y z 2x 2y 2z a+2x b+2y c+2z Official Time: 22:24:28 SUBMIT AND MARK
U is a 2 x 2 orthogonal matrix of determinant -1. Find 5 · [0, 1] · U if 5 · [1,0] · U = (-3,4]. 2. Let M = [[144, 18], [18, 171]]. Notice that 180 is an eigenvalue of M. Let U be an orthogonal matrix such that U-MU is diagonal, the first column of U has positive entries, and det(U) = 1. Find 145 · U.