Question 19 [10 points] If the determinant of the first matrix below is as given, find...
12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal.
12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal.
2. Find solutions to the values of x, y, and z using the matrix inversion technique discussed in this course. Please show all intermediate steps. x + 2y + 2z=1 2x+y=-2 +22 2x+z=1+2y
(6 points) Evaluate the following system using the augmented matrix method. When performing row reduction, be sure to indicate your row operations. x 2x -x + 2y + 5y + 4y – + – 2= z = 2z = -3 1 3 (12 points) Evaluate the following system using Gauss-Jordan elimination. When per- forming row reduction, be sure to indicate your row operations. 2x x -x (a) – + + y + z = y + 2z = 3y +...
5. (10 points) Find the determinant of the given matrix A by using cofactor expansion. Then find the determinant of A. 1 2 A= | -2 3 3 -5 5 1 7 0 /
Use expansion by cofactors to find the determinant of the matrix. w х у z 27 -18 15 24 -32 24 -10 18 -35 40 32 -22 X Need Help? Read It Watch It Submit Answer
Question 12 [10 points] Find an invertible matrix P and a diagonal matrix D such that P-lAP=D. | 9 6 -2 A= -20 -13 4 | -24 -12 3 Tooo oool P= 0 0 0 D = 0 0 0 0 0 0 | 0 0 0 Official Time: 19:51:55 CS Scanned with CamScanner
6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix multiplication EB (b) Compute the determinant of EB using the cofactor expansion along the 1st row of the matrix, and show that the determinant is equal to -det(B) (MUST use the cofactor expansion, no points will be given for other meth- ods.) Hint: Same, don't expand everything out, you will be drown in a sea of bij, you should look at the cofactor expansion...
LarPCalc8 8.1.012 45 points 1. Determine the order of the matrix. 47 15 0 -1 0 3 3 6 7 -3 1 O-15 points LarPCalc8 8.1.020. 2. Write the augmented matrix for the system of linear equations. {Sx 4y-2z 24 -21y +8z -3 8x + O-15 points LarPCalc8 8.1.022 My Nete 3. Write the system of linear equations represented by the augmented matrix. (Use the variables x, y, z, and w, if applicable.) 7 -5-4 3 39 8 O-5 points...
(1 point a. The linear transformation T : R2 → R2 is given by: Ti (x, y) = (2x + 9y, 4x + 19y). Find T1x, y). 「-i(x, y) =( x+ y, x+ b. The linear transformation T2 : R' → R' is given by: T2(x, y, z) (x + 2z,2r +y, 2y +z) Find (x, y, z). T2-1(x,y,z)=( x+ y+ z, x+ y+ z, x+ y+ z)
Find the standard matrix for the linear transformation T. T(x, y) = (3x + 2y, 3x – 2y) Submit Answer [-70.71 Points] DETAILS LARLINALG8 6.3.007. Use the standard matrix for the linear transformation T to find the image of the vector v. T(x, y, z) = (8x + y,7y - z), v = (0, 1, -1) T(v)