matrix A is
2 | 9 |
4 | 19 |
add the Identity Matrix to the right of our matrix
2 | 9 | 1 | 0 |
4 | 19 | 0 | 1 |
by Gauss-Jordan Elimination
Divide row1 by 2
1 | 9/2 | 1/2 | 0 |
4 | 19 | 0 | 1 |
Add (-4 * row1) to row2
1 | 9/2 | 1/2 | 0 |
0 | 1 | -2 | 1 |
Add (-9/2 * row2) to row1
1 | 0 | 19/2 | -9/2 |
0 | 1 | -2 | 1 |
inverse matrix:
19/2 | -9/2 |
-2 | 1 |
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matrix A is
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1 | 0 | 2 |
2 | 1 | 0 |
0 | 2 | 1 |
add the Identity Matrix to the right of our matrix
1 | 0 | 2 | 1 | 0 | 0 |
2 | 1 | 0 | 0 | 1 | 0 |
0 | 2 | 1 | 0 | 0 | 1 |
by Gauss-Jordan Elimination
Add (-2 * row1) to row2
1 | 0 | 2 | 1 | 0 | 0 |
0 | 1 | -4 | -2 | 1 | 0 |
0 | 2 | 1 | 0 | 0 | 1 |
Add (-2 * row2) to row3
1 | 0 | 2 | 1 | 0 | 0 |
0 | 1 | -4 | -2 | 1 | 0 |
0 | 0 | 9 | 4 | -2 | 1 |
Divide row3 by 9
1 | 0 | 2 | 1 | 0 | 0 |
0 | 1 | -4 | -2 | 1 | 0 |
0 | 0 | 1 | 4/9 | -2/9 | 1/9 |
Add (4 * row3) to row2
1 | 0 | 2 | 1 | 0 | 0 |
0 | 1 | 0 | -2/9 | 1/9 | 4/9 |
0 | 0 | 1 | 4/9 | -2/9 | 1/9 |
Add (-2 * row3) to row1
1 | 0 | 0 | 1/9 | 4/9 | -2/9 |
0 | 1 | 0 | -2/9 | 1/9 | 4/9 |
0 | 0 | 1 | 4/9 | -2/9 | 1/9 |
inverse matrix:
1/9 | 4/9 | -2/9 |
-2/9 | 1/9 | 4/9 |
4/9 | -2/9 | 1/9 |
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(1 point a. The linear transformation T : R2 → R2 is given by: Ti (x,...
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.
Problem 2 [10pts] Let f : R3 + R2 be a linear transformation given by f((x, y, z) = (–2x + 2y +z, -x +2y). Find the matrix that corresponds to f with respect to the canonical bases of R3 and R2.
Find the standard matrix for the linear transformation T. T(x, y, z) = (x - 2z, 2y = z) 11
Determine whether or not the following transformation T :V + W is a linear transformation. If T is not a linear transformation, provide a counter example. If it is, then: (i) find the nullspace N(T) and nullity of T, (ii) find the range R(T) and rank of T, (iii) determine if T is one-to-one, (iv) determine if T is onto. : (a) T: R3 + R2 defined by T(x, y, z) = (2x, y, z) (b) T: R2 + R2...
1. Consider the transformation given by T(x, y, z)- (2z 3z+) (a) Show that T is a linear transformation (b) Find the domain and range of T (c) Find the number of columns and r for T. (d) Find the standard matrix for T.
Linear Algebra! Practice exam #1 question 1 Thanks for sloving! 1- Transformations (3 points each) a) Given a linear transformation T :N" N" T(x,y)-(x-y,x+y) and B= {< l, 0>.< 1,1 >} , B = {< l, l>,< 0, l>} V,-< 2, l> Find V,T,and TVg) b) Given a linear transformation T:n'->n2 T(x,y,2)-(x-z,x +2y)and V =< 2,-I, I> B= {<l, 0, 1>.< 1, 1, 0 >, < 0, l, 0 >}, B' = {<l, l >, < 0, 1 >} Find...
Is the transformation, T, given below a Linear Transformation where T: R2 -> R2 [:] - [+*] (y + 1)2 1 x - 1 1
Question Let T : R2 + Rº be a linear transformation with PT(x) = x2 – 1. Determine/Compute the linear transformation T2 : R2 + R?, UH T(T(v)).
2. Consider the linear functions f: R3 → R2, 9: R3 R3, h: R2 + R and i: R3 → R4 given by: [ 5x – 72 1 * +54 +92 [2x + 3y +z] y = 3 +9y + 7z IL -+2y 2. + 2y + i i = y +22 |2y – z] (14 (a) Write them as matrices. (b) Which are the compositions we can do using two different functions from above? Do them using matrix multiplication.
(1 point) Let T : P3-> P3 be the linear transformation such that Find T(1). T(x). T(r2), and T(az2 + bz+ c), where a, b, and c are arbitrary real numbers. T(1) = T(z) = T(r2) Note: You can earn partial credit on this problem.