![1. (6 points) Let S be a subspace of R3 spanned by the columns of the matrix [1 2 0 1 1] 2 4 1 1 0 3 6 1 2 1 Find a basis of](http://img.homeworklib.com/questions/a1bdff80-ac34-11eb-9ff6-174adc97e1c9.png?x-oss-process=image/resize,w_560)
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1. (6 points) Let S be a subspace of R3 spanned...
Linear Algebra Problem! 1. Let U be the subspace of R3 given by 11 + 12...
Linear Algebra Problem!
1. Let U be the subspace of R3 given by 11 + 12 - 213 = 0. for U. Justify that is an ordered basis. What is the a) Find an ordered basis dimension of U? b) Let ū= (1,1,1). Show that ✓ EU and find the B-coordinate vector (Ū3 = C:(Ū), where Ce: U + R2 is the B-coordinate transformation.
Find a basis for the subspace of R3 spanned by S. S = {(4, 4, 9),...
Find a basis for the subspace of R3 spanned by S. S = {(4, 4, 9), (1, 1, 3), (1, 1, 1)} STEP 1: Find the reduced row-echelon form of the matrix whose rows are the vectors in S. 1 0 0 1 0 0 0 x STEP 2: Determine a basis that spans S. 35E
11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1...
11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1 and 4 Find the projection matrix P that projects vectors in R3 onto W
6. Find a basis for the subspace of R3 spanned by S (42,30,54), (14,10, 18),(7,5,6)). 7....
6. Find a basis for the subspace of R3 spanned by S (42,30,54), (14,10, 18),(7,5,6)). 7. Given that [xlg [4,5,3]', the coordinate matrix of x relative to a (nonstandard) basis B((,1,0(1,0,1),(0,0,0)). Find the coordinate vector of x relative to the standard basis in R3 8. Find the coordinate matrix of x=(-3,28,6) in Rs relative to the basis B=((3,8,0),(5,0,11),( 1,5,7), 9. Find the transition matrix from B ((1,7),(-2, -2))to B'- ((-28,0),(-4,4)) 10 Perform a rotation of axes to eliminate the xy-term,...
4. Let T be the linear operator on F which is represented in the standard ordered basis by the matrix c0 0 01 Let W be the nll space of T - c/. (a) Prove that W is the subspace spanned by 4 (b) F...
4. Let T be the linear operator on F which is represented in the standard ordered basis by the matrix c0 0 01 Let W be the nll space of T - c/. (a) Prove that W is the subspace spanned by 4 (b) Find the monic generators of the ideals S(u;W), S(q;W), s(G;W), 1
4. Let T be the linear operator on F which is represented in the standard ordered basis by the matrix c0 0 01 Let W...
linear algebra: show all work please ned by Xi = I Find a basis 4. Let...
linear algebra: show all work please
ned by Xi = I Find a basis 4. Let S be the subspace of R4 spanned b (1,0, 2, 1)? and x2 = (0, 1, 3, -2)7. Find for St.
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1...
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V) 0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)
5. Suppose that S is the subspace in R3 spanned by the two vectors aj =...
5. Suppose that S is the subspace in R3 spanned by the two vectors aj = 1 , a2 = 0 . (a) Find the projection matrix P onto S. (b) Find the projection p of b onto S where ſi b= -1 (c) If b is in S then what is Pb? (d) If b is in St then what is Pb?
Let W be the subspace of R3 spanned by the vectors ⎡⎣⎢113⎤⎦⎥ and ⎡⎣⎢4615⎤⎦⎥. Find the projection matrix P that project...
Let W be the subspace of R3 spanned by the vectors ⎡⎣⎢113⎤⎦⎥ and ⎡⎣⎢4615⎤⎦⎥. Find the projection matrix P that projects vectors in R3 onto W.
Linear Algebra Problem!
1. Let U be the subspace of R3 given by 11 + 12 - 213 = 0. for U. Justify that is an ordered basis. What is the a) Find an ordered basis dimension of U? b) Let ū= (1,1,1). Show that ✓ EU and find the B-coordinate vector (Ū3 = C:(Ū), where Ce: U + R2 is the B-coordinate transformation.
Find a basis for the subspace of R3 spanned by S. S = {(4, 4, 9), (1, 1, 3), (1, 1, 1)} STEP 1: Find the reduced row-echelon form of the matrix whose rows are the vectors in S. 1 0 0 1 0 0 0 x STEP 2: Determine a basis that spans S. 35E
11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1 and 4 Find the projection matrix P that projects vectors in R3 onto W
6. Find a basis for the subspace of R3 spanned by S (42,30,54), (14,10, 18),(7,5,6)). 7. Given that [xlg [4,5,3]', the coordinate matrix of x relative to a (nonstandard) basis B((,1,0(1,0,1),(0,0,0)). Find the coordinate vector of x relative to the standard basis in R3 8. Find the coordinate matrix of x=(-3,28,6) in Rs relative to the basis B=((3,8,0),(5,0,11),( 1,5,7), 9. Find the transition matrix from B ((1,7),(-2, -2))to B'- ((-28,0),(-4,4)) 10 Perform a rotation of axes to eliminate the xy-term,...
4. Let T be the linear operator on F which is represented in the standard ordered basis by the matrix c0 0 01 Let W be the nll space of T - c/. (a) Prove that W is the subspace spanned by 4 (b) Find the monic generators of the ideals S(u;W), S(q;W), s(G;W), 1
4. Let T be the linear operator on F which is represented in the standard ordered basis by the matrix c0 0 01 Let W...
linear algebra: show all work please
ned by Xi = I Find a basis 4. Let S be the subspace of R4 spanned b (1,0, 2, 1)? and x2 = (0, 1, 3, -2)7. Find for St.
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)
5. Suppose that S is the subspace in R3 spanned by the two vectors aj = 1 , a2 = 0 . (a) Find the projection matrix P onto S. (b) Find the projection p of b onto S where ſi b= -1 (c) If b is in S then what is Pb? (d) If b is in St then what is Pb?
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