Find a basis for the subspace of R4 spanned by S. S = {(3, 9, –3, 53), (-4, 3, 4, –3), (8, –4, –8, 17), (0, –4, 0, 15)}

Q: Find the orthogonal projection of 9. -3 = 4 onto the subspace W of Rª spanned by -3 -4 3 and 6 -3…

A: Solution:-

Q: Find the dimension of the subspace W of R* spanned by set S = {(3,0,1,–2), (–5,4,9,2), (–1,2,5,0)} .

A:

Q: Find a basis for the subspace of Rª spanned by S. S = {(2, 9, -2, 53), (-4, 2, 4, –2), (8, –4, -8,…

A:

Q: Find a basis for the subspace of R* spanned by the following set. (Enter your answers as a…

A:

Q: 1. Compute the orthogonal complement of each of the following subspace of the given vecto (a) W =…

A: We have to find orthogonal complement of given subspace: Concept: If x is orthogonal vector to…

Q: . Give a basis for the orthogonal complement of each of the following subspaces of Rª. a. V = Span…

A: We will find out the required basis.

Q: Find a basis for the subspace of R4 spanned by S.S = { (6, −3, 6, 34), (3, −2, 3, 19), (8, 3, −9,…

A: Given: S = { (6, −3, 6, 34), (3, −2, 3, 19), (8, 3, −9, 6), (−2, 0, 6, −5)} To find: Basis spanned…

Q: Find a basis for the subspace of Rª spanned by S. S = {(29, –14, 6, –12), (-14, 7, –3, 6), (4, –2,…

A:

Q: Find a basis for each subspace... [5r-3s, 2r, 0, -4s] ER^4:r and s are scalars

A:

Q: Let S be the subspace of R4 spanned by x1 = (1, 0,−2, 1)T and x2 = (0, 1, 3,−2)T . Find a basis for…

A:

Q: Consider the following subspaces of R': U = span[(1,3, -2,2), (1,4, –3,4), (2,3,-1,-2)] W =…

A:

Q: Find a basis for the subspace of R* spanned by S. S = {(-11, -6, -4, -8), (-6, -3, -2, -4), (4, 2,…

A:

Q: Find a basis for sunspaces of R4  a)the vector for which is x1=2x4 b)the  subspace spanned by…

A:

Q: Find a basis for the subspace of R* spanned by S. S = {(-20, –7, 2, –4), (21, 7, –2, 4), (-9, –3, 1,…

A: We have given set of vectors ,  S = -20 , -7 , 2 , -4 , 21 , 7 , -2 , 4 , -9 , -3 , 1 , -2 , -18 ,…

Q: Find a basis for the subspace of R* spanned by the given vectors. (1,1,6,-7), (2,0,2-2), (3,-1,1,27)…

A: To find the basis for the subspace of R4 spanned by the vectors (1, 1, -6, -7), (2, 0, 2, -2), and…

Q: In R4 , find the dimension of the subspace spanned by the vectors {(1, 1, 1, 1)T , (1, 2, 2, 2)T ,…

A: Given vectors are {(1, 1, 1, 1)T , (1, 2, 2, 2)T , (1, 1, 2, 1)T , (2, 2, 3, 2)T , (4, 5, 6, 5)T }.

Q: Find a basis for the subspace of R* spanned by S. S = {(43, -21, 6, 12), (-14, 7, -2, –4), (6, –3,…

A:

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 9, -2, 53), (-4, 2, 4, –2), (8, –4, –8,…

A:

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 9, -2, 53), (-5, 2, 5, –2), (8, –5, –8,…

A:

Q: Find a basis for the subspace of R4 spanned by S. S = {(-11, 6, 4, 8), (-6, 3, 2, 4), (-2, 1, 1, 2),…

A:

Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 4, 7), (-1, 5, 7), (2, 5, 1)}

A: The matrix form the vectors is: A=1-12455771

Q: Find a basis for the subspace of R3 spanned by S. S = {(5, 9, 9), (1, 2, 2), (1, 1, 1)}

A: To find the basis for the subspace of R3 spanned by the given set of vectors S.

Q: Find a basis for the subspace of R* spanned by S. S = {(64, -21, 9, 27), (-21, 7, -3, -9), (6, -2,…

A: B is called the basis for the subspace of ℝ4 spanned by S  if i) B is linearly independent  ii) B…

Q: Find a basis and calculate the dimension of the following subspace of R*. span{(-2,0,3,1), (1,2, –…

A: Given subspace is S=-2,0,3,1, 1,2,-1,0, -2,8,5,3, -1,2,2,1 and we have to find the basis and…

Q: Find a basis for the subspace of R4 spanned by S. S = {(3, 1, 1, 3), (-2, –1, -1, -3), (4, 2, 1, 3),…

A: Let S=3, 1, 1, 3, -2, -1, -1, -3, 4, 2, 1, 3, -12, -6, -3, -8

Q: Find a basis for the subspace of R° spanned by the following vectors. 6. 18 -3 -3 6 6. -18 -18 14…

A: We solve this by row reduced echolon  form

Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0, 3), (2, 1, –2), (0, – 1, 8),…

A:

Q: Find the orthogonal projection of -19 5 -5 -12 onto the subspace W of IRª spanned by 1 -4 and 5 10

A: As per the orthogonal Decomposition  theorem  Let us assume W is a subspace of Rn then each y in Rn…

Q: Determine which of the following subspaces of R3 are identical: U1= span[ (1,1,-1), (2,3,-1),…

A: if the dimension of U, V and U+V are the same, then U and V both are identical. Dimension U1

Q: Is the following set of vectors in R 3 linearly dependent: {(1, 0, 3),(2, 1, -2),(0, -1, 8),(7, 2,…

A: The solution is given as

Q: Find a basis for the subspace of R* spanned by S. S = {(5, 9, –5, 53), (-3, 5, 3, -5), (8, –3, –8,…

A: A matrix being in row echelon form means that Gaussian elimination has operated on the rows, and…

Q: Find a basis for the subspace of R* spanned by S. S = {(2, 5, -3, -5), (-2, -3, 2, -2), (1, 3, - 2,…

A:

Q: 4. Find a basis for the intersection of the subspaces V = Span ((1, 0, 1, 1), (2, 1, 1, 2)) and W =…

A:

Q: Find a basis of the following subspace of R“. span {(-1, 2, 1, O), (2, 0, 3, –1), (4, 4, 11, -3),…

A:

Q: Find a basis for the subspace of R4 spanned by the given vectors. (1,1,-6,-7), (2,0,2,-2),…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, –3, -2), (-2, –3, 2, –5), (1, 3, -2,…

A:

Q: 5. Let S = {x + 1,x2 – 2, x – 1,3}. Find a basis for the subspace W that is spanned by S.

A:

Q: Find the dimension of the subspace W of R4 spanned by S = {v1, v2, v3} = {(−1, 2, 5, 0), (3, 0, 1,…

A: Dimension of a subspace W is given by the number of linearly independent vectors in the basis of W,…

Q: Find a basis for the subspace of R" spanned by S. S = {(43, -21, 6, 18), (-14, 7, -2, -6), (6, –3,…

A: Subspace of  ℝ4  spanned by S is               S = { (43,-21,6,18) ,(-14,7,-2,-6) ,…

Q: Find a basis for the subspace of Rª spanned by S. S = {(2, 5, –3, –5), (-2, –3, 2, –2), (1, 3, –2,…

A: This question related to linear algebra's topic basis of vector space.

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, -3, -4), (-2, -3, 2, -2), (1, 3, -2,…

A:

Q: Find a basis for the subspace of R4 spanned by the given vectors. (1,1,-4,-2), (3,0,3,-3),…

A:

Q: Find a basis for the subspace of R4 spanned by S.S = { (2, 9, −2, 53), (−3, 2, 3, −2), (8, −3, −8,…

A: To Find a basis for the subspace of  R4 spanned by S.…

Q: Find a basis for the subspace of RA spanned by S. S = {(2, 5, -3, -5), (-2, -3, 2, -2), (1, 3, -2,…

A:

Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 5, 7), (-1, 6, 7), (2, 6, 1)}

A: Write the given set of elements as the rows  to form a 3x3 matrix. The space spanned by the rows of…

Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, -3, -5), (-2, -3, 2, -4), (1, 3, -2,…

A: We have to find the basis.

Q: 2. Find the dimension of the subspace of R³ spanned by the following set of vectors. {(1,5, 6),…

A:

Q: Find a basis for the subspace of R spanned by S. S = {(2, 5, -3,-4), (-2, -3, 2,-2), (1, 3, -2, 4),…

A: Given that S=2,5,-3,-4,-2,-3,2,-2,1,3,-2,4,-1,-5,3,2.

Q: Find a basis for the subspace of R spanned by the following vectors. 7 4 2 2 18 -3 6 6 18 18 12 14…

A: