In each of the following determine if the /1 111-4) [1 2 1 -2 -2 |...
(d) (4 points) Let T : R² + Rº be the transformation that rotates any vector 90 degrees counterclockwise. Let A be the standard matrix for T. Is A diagonalizable over R? What about over C? (e) (3 points) Let T : R4 → R4 be given by T(x) = Ax, A = 3 -1 7 12 0 0 0 4 0 0 5 4 0 4 2 1 Is E Im(T)? 3 (f) (9 points) Let U be a...
Question 5 True of False part II: 5 problems, 2 points each. (6). Let w be the x-y plain of R3, then wlis any line that is orthogonal to w. (Select) (7). Let A be a 3 x 3 non-invertible matrix. If Ahas eigenvalues 1 and 2, then A is diagonalizable. Sele (8). If an x n matrix A is diagonalizable, then n eigenvectors of A form a basis of " [Select] (9). Letzbean x 1 vector. Then all matrices...
(a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5 6 2 2 3 -1 A=158 O 11 and B-1084 7 1o-2 3 21 6 (5+5 (b) () For any n x I vector a 0, show that a (ii) Find the g-inverse of the vector a, where a' = [1 a'a 5 2] 3 1 (a) Reduce the following matrices to diagonal form and find a g-inverse of each 120-11 4 5...
(1) For each of the following functions, determine if it is injective and determine if it is surjective. Justify your answer. (a) f : R → R, f(x) = 2x + 3. (b) g : R → R 2 , g(x) = (2x, 3x −1). (c) h : R 2 → R, h((x, y)) = x + y + 1. (d) j : {1, 2, 3} → {4, 5, 6}, j(1) = 5, j(2) = 4, j(3) = 6. (2)...
please anyone answer all the questions as soon please 2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
determine which elements land in each region of the following venn diagram Given that U = {1, 2, 3, ..., 11, 12, 13} A = {1, 2, 4, 5, 9, 10} B = {3,7,8,9} Determine which elements land in each region of the following Venn Diagram. LIST the elements in each of the following regions in set notation: Hint Region I- Region II - Region III - Region IV- Hint Hint Hint Points possible: 5 This is attempt 1 of...
(4) The following is the singular value decomposition of a 3 x 4 matrix A with some entries not given 1/3 -2/V5 1/v5 2/3 2/3 3 0 12/13 5/13 3/5 4/5 5/13 12/13 0 0 A 0 2 0 0 0 0 0 0 0 (a) What are the eigenvalues of AAT? of ATA? What is the rank of A? 1 2 (b) Find a non-zero vector w such that AAT = 9w. such that ATAu 4u. (c) Find a...
Refer to the below Enzyme activity data (Table 4) to determine the following: (1.5 pts each) a) Vmax b) why is the velocity v constant at [S] greater than 2 x 10-3 M? c) what is the free [E] at [S] = 2 x 10-2 M? 2. SI (mol/L 2 x 10-l 2 x 10-2 2 x 10-3 2 x 104 5 x 10-4 1,3 x 10-5 ol/min 60.00 60.00 60.00 48.00 45.00 2.00 Table 4. Enzyme activity assay data...
* Problem #4: Pivot the following matrix, 1-4 12 -4 -20 2 1 -2 -2 2 1 2 4 Thira about the entry 011: ſi -3 1 5 1 [i -3 1 5 [i -3 1 51 [1 -3 1 5 1 (A) O 7 -4 -12 (B) O 7 -3 -12 (C) 0 7 -3 -9 ( D O 7 -4 -11 Lo 7 0 -6] LO 7 3 -3 ] [O 7 0 -3] LO 8 0 -6]...
please answer the question 2) (1 point) For each transformation below, determine a basis for (Range(T)) Note that if you do not need a basis vector, then write o for entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector 9 Let 7 [a ] la 250e6d 20 +56 + 10 +14d 2a +65 +2c + 160 4a +(12)+( 4)c+(32) d -30 +...