Homework Answers
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Consider T: RR with BREF 3 5 2 1 10 4 3 -4 -1 -20 -6...
Consider T: RR with BREF 3 5 2 1 10 4 3 -4 -1 -20 -6 1 0 0 0 05 Doints) Find a basis for image(T). What is dim(image(T))? (4 points) Convert image(T) to relation form.
R is defined by T (7) = AZ mation T: R3 4. [20 marks) A linear...
R is defined by T (7) = AZ mation T: R3 4. [20 marks) A linear transformation T: R with A given as follows: A= [ 1 -2 1 3 0 -21 1 6 -2 -5 J (1). (8 marks) A vector in R is given as follows = -1 determine the image of 7 under T. 12 marks) Find a vector in Rwhose image under T is the following vector 6 -17 7 = 7 L -3 or demonstrate...
-4 0 -1 1 1 2 7 6 (1 pt) Let A 1 5 -3 -1...
-4 0 -1 1 1 2 7 6 (1 pt) Let A 1 5 -3 -1 3 13 -1 -1 Find orthogonal bases of the kernel and image of A 10 -1 1 2 Basis of the kernel: -1 1 -1 3 -3 1 8 Basis of the image: -1 1 -1 7 (1 pt) Perform the Gram-Schmidt process on the following sequence of vectors. -3 -2 6 -3 6 y= -5 х — 3 -4 3 1 2 -2...
_Determine which of these sets is a basis for R3. 1 - 1 ^ {[:] 7]...
_Determine which of these sets is a basis for R3. 1 - 1 ^ {[:] 7] [8]} - {[7] | c{[7] [8] [8]} » {[![10]} Determine the dimension of the subspace W = span {V1, V2, V3, V4} where A. dim(W)=1 B. dim(W) = 2 C. dim(W) = 3 D. dim(W) = 4 8 Determine both the rank and nullity of the matrix A= [1 0 1 | 2 -3 4 -2 -2 2 -4 1 0 3 -4 2...
Question 1.2 Let T : R3 ? R2 be a linear transformation given by T (x)...
Question 1.2 Let T : R3 ? R2 be a linear transformation given by T (x) = Ax, where 1 0 2 -1 1 5 1) Find a basis for the kernel of T. 2) Determine the dimension of the kernel of T 3) Find a basis for the image(range) of T. 4) Determine the dimension of the image(range) of T. 5) Determine if it is a surjection or injection or both. 2 6) Determine whether or not v |0|...
eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8...
eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8 (a) Find a basis B for the null space of A. Hint: you need to verify that the vectors you propose 20 actually form a basis for the null space. (Recall: (1) the null space of A consists of all x e R with Ax = 0, and (2) the matrix equation Ax = 0 is equivalent to a certain system of linear equations.)...
consider T(x）= A (x) [1 2 0 3 6 1 2 4 1 1 2 3...
consider T(x）= A (x)
[1 2 0 3 6 1 2 4 1 1 2 3 -1 2 9 2 1 5 10 11 0 (a) Find a basis for the nullspace (kernel) of T. (b) Find a basis for the range of T. (c) What are the values of the rank and nullity?
-3 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6...
-3 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 78 Re A sinusoid has an associated phasor shown in the graph above. Find the sinusoid's formula, in the form z t = Aco (2x100e十0) Enter the formula below. Give the phase value in radians between r(t) π and π cos(2100t+
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï....
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï. Find the images of u Define the linear transformation T : R- and y 4 under = - T. T(M TM =
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï. Find the images of u Define the linear transformation T : R- and y 4 under = - T. T(M TM =
If A=[(1, 2,1) (2, 0, 0) (0, 5, 0)] A: R3->R3 1) Find the row reduced echelon form of A 2) Find the image of A 3) Fin...
If A=[(1, 2,1) (2, 0, 0) (0, 5, 0)] A: R3->R3 1) Find the row reduced echelon form of A 2) Find the image of A 3) Find a nonzero vector in ker(A)
Consider T: RR with BREF 3 5 2 1 10 4 3 -4 -1 -20 -6 1 0 0 0 05 Doints) Find a basis for image(T). What is dim(image(T))? (4 points) Convert image(T) to relation form.
R is defined by T (7) = AZ mation T: R3 4. [20 marks) A linear transformation T: R with A given as follows: A= [ 1 -2 1 3 0 -21 1 6 -2 -5 J (1). (8 marks) A vector in R is given as follows = -1 determine the image of 7 under T. 12 marks) Find a vector in Rwhose image under T is the following vector 6 -17 7 = 7 L -3 or demonstrate...
-4 0 -1 1 1 2 7 6 (1 pt) Let A 1 5 -3 -1 3 13 -1 -1 Find orthogonal bases of the kernel and image of A 10 -1 1 2 Basis of the kernel: -1 1 -1 3 -3 1 8 Basis of the image: -1 1 -1 7 (1 pt) Perform the Gram-Schmidt process on the following sequence of vectors. -3 -2 6 -3 6 y= -5 х — 3 -4 3 1 2 -2...
_Determine which of these sets is a basis for R3. 1 - 1 ^ {[:] 7] [8]} - {[7] | c{[7] [8] [8]} » {[![10]} Determine the dimension of the subspace W = span {V1, V2, V3, V4} where A. dim(W)=1 B. dim(W) = 2 C. dim(W) = 3 D. dim(W) = 4 8 Determine both the rank and nullity of the matrix A= [1 0 1 | 2 -3 4 -2 -2 2 -4 1 0 3 -4 2...
Question 1.2 Let T : R3 ? R2 be a linear transformation given by T (x) = Ax, where 1 0 2 -1 1 5 1) Find a basis for the kernel of T. 2) Determine the dimension of the kernel of T 3) Find a basis for the image(range) of T. 4) Determine the dimension of the image(range) of T. 5) Determine if it is a surjection or injection or both. 2 6) Determine whether or not v |0|...
eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8 (a) Find a basis B for the null space of A. Hint: you need to verify that the vectors you propose 20 actually form a basis for the null space. (Recall: (1) the null space of A consists of all x e R with Ax = 0, and (2) the matrix equation Ax = 0 is equivalent to a certain system of linear equations.)...
consider T(x）= A (x)
[1 2 0 3 6 1 2 4 1 1 2 3 -1 2 9 2 1 5 10 11 0 (a) Find a basis for the nullspace (kernel) of T. (b) Find a basis for the range of T. (c) What are the values of the rank and nullity?
-3 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 78 Re A sinusoid has an associated phasor shown in the graph above. Find the sinusoid's formula, in the form z t = Aco (2x100e十0) Enter the formula below. Give the phase value in radians between r(t) π and π cos(2100t+
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï. Find the images of u Define the linear transformation T : R- and y 4 under = - T. T(M TM =
(2 points) Let -1 7 A = -9 5 -8 -6 a R3 by T(x Aï. Find the images of u Define the linear transformation T : R- and y 4 under = - T. T(M TM =
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