Homework Answers
Question 1 Question 2 Let u, v, w be three vectors in R4 with the property...
Question 1
Question 2
Let u, v, w be three vectors in R4 with the property that 4u - 30+2w = 0. Let A be the 4 x 2 matrix whose columns are u and u (in that order). Find a solution to the equation Ac =W. Let 1 -2 0 3 A=1 -2 2-1 2 -4 1 4 Find a list of vectors whose span is the set of solutions to Ax = 0. 1 1 Enter the list...
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x...
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x, y) |z 2 0,y S 0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? H contains the zero vector of V 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H,...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
Write each vector as a linear combination of the vectors in S. (If not possible, enter...
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = (6, -7, 8, 6), (4, 6, -4, 1)} (a) (18, 43, -32, 0) -1 6 + 35 89 -14, 4 (b) V = 2. V = 1 23 -4, -14, 8 57 (c) W = 8 61 73 s X W = + 6 24 13 -2, 3 4 (d) Z = 4, | »2 + X
Let S={2,3+x,1−x2}, p(x)=2−x−x2 and V=P2 (a) If possible, express p(x)as a linear combination of vectors in...
Let S={2,3+x,1−x2}, p(x)=2−x−x2 and V=P2 (a) If possible, express p(x)as a linear combination of vectors in S. (b) By justifying your answer, determine whether the set S is linearly independent or linearly dependent. (c) By justifying your answer, determine whether the set S is a basis for P2 Please solve it in very detail, and make sure it is correct.
Find x- and y-components of the following vectors. 1) v⃗ =(9.0m/s,negativey−direction) Express your answers using two...
Find x- and y-components of the following
vectors.
1) v⃗ =(9.0m/s,negativey−direction)
Express your answers using two significant figures. Enter your
answers numerically separated by a comma
2) a⃗ =(24m/s2,58∘belowpositivex−axis)
Express your answers using two significant figures. Enter your
answers numerically separated by a comma.
3)
F⃗ =(70N,47.5∘counterclockwisefrompositivey−axis)
Express your answers using two significant figures. Enter your
answers numerically separated by a comma.
Find x- and y-components of the following vectors. - Part A V = (9.0m/s, negative y direction) Express...
can anybody explain how to do #9 by using the theorem 2.7? i know the vectors...
can anybody explain how to do #9 by using the theorem
2.7?
i know the vectors in those matrices are linearly independent,
span, and are bases, but i do not know how to show them with the
theorem 2.7
a matrix ever, the the col- ons of B. e rela- In Exercises 6-9, use Theorem 2.7 to determine which of the following sets of vectors are linearly independent, which span, and which are bases. 6. In R2t], bi = 1+t...
Let S = {2,3 + x, 1 – x2}, p(x) = 2 - x - x2...
Let S = {2,3 + x, 1 – x2}, p(x) = 2 - x - x2 and V = P2. (a) If possible, express p(x) as a linear combination of vectors in S. (b) By justifying your answer, determine whether the set S is linearly independent or linearly dependent. (c) By justifying your answer, determine whether the set S is a basis for P2.
Consider the function below. x)= (x-4)2 (a) Find the vertical asymptote(s). (Enter your answers as a...
Consider the function below. x)= (x-4)2 (a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list. If an a er does not exist, enter DNE.) answ x Find the horizontal asymptote(s). (Enter your an comma-separated list. If an answer does not exist, enter DNE.) s wers as a y (b) Find the interval(s) where the function is increasing. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) Find the interval(s) where the function...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
Question 1
Question 2
Let u, v, w be three vectors in R4 with the property that 4u - 30+2w = 0. Let A be the 4 x 2 matrix whose columns are u and u (in that order). Find a solution to the equation Ac =W. Let 1 -2 0 3 A=1 -2 2-1 2 -4 1 4 Find a list of vectors whose span is the set of solutions to Ax = 0. 1 1 Enter the list...
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x, y) |z 2 0,y S 0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? H contains the zero vector of V 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H,...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = (6, -7, 8, 6), (4, 6, -4, 1)} (a) (18, 43, -32, 0) -1 6 + 35 89 -14, 4 (b) V = 2. V = 1 23 -4, -14, 8 57 (c) W = 8 61 73 s X W = + 6 24 13 -2, 3 4 (d) Z = 4, | »2 + X
Find x- and y-components of the following
vectors.
1) v⃗ =(9.0m/s,negativey−direction)
Express your answers using two significant figures. Enter your
answers numerically separated by a comma
2) a⃗ =(24m/s2,58∘belowpositivex−axis)
Express your answers using two significant figures. Enter your
answers numerically separated by a comma.
3)
F⃗ =(70N,47.5∘counterclockwisefrompositivey−axis)
Express your answers using two significant figures. Enter your
answers numerically separated by a comma.
Find x- and y-components of the following vectors. - Part A V = (9.0m/s, negative y direction) Express...
can anybody explain how to do #9 by using the theorem
2.7?
i know the vectors in those matrices are linearly independent,
span, and are bases, but i do not know how to show them with the
theorem 2.7
a matrix ever, the the col- ons of B. e rela- In Exercises 6-9, use Theorem 2.7 to determine which of the following sets of vectors are linearly independent, which span, and which are bases. 6. In R2t], bi = 1+t...
Let S = {2,3 + x, 1 – x2}, p(x) = 2 - x - x2 and V = P2. (a) If possible, express p(x) as a linear combination of vectors in S. (b) By justifying your answer, determine whether the set S is linearly independent or linearly dependent. (c) By justifying your answer, determine whether the set S is a basis for P2.
Consider the function below. x)= (x-4)2 (a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list. If an a er does not exist, enter DNE.) answ x Find the horizontal asymptote(s). (Enter your an comma-separated list. If an answer does not exist, enter DNE.) s wers as a y (b) Find the interval(s) where the function is increasing. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) Find the interval(s) where the function...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
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