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

Q: Find a basis for the subspace of R3 spanned by S = {(2,3, -1), (1,3, -9), (0,1,5)}

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

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

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

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Q: Find the standard matrix for the orthogonal projection of R3 onto the subspace spanned by aj=(1,1)…

A: The vectors that span the subspace are a1=1, 1 and a2=0, 1. The normalising vectors are 12, 12 and…

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

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Q: Find a basis for the subspace of IR spanned by the following vectors. 6. 10 1 1 -2 -6 -10

A: We will reduce the dependence of the set by checking if (and how many) any vectors are dependent on…

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

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Q: Find a basis for the orthogonal complement of the subspace of R* spanned by the vectors. V1= (1, 3,…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(5, 9, −5, 53), (−4, 5, 4, −5), (8, −4, −8,…

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

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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: Let H be the collection of all 2 × 4 matrices whose second and fourth columns are equal. Show that H…

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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 = {(2, 5, -3, -2), (-2, –3, 2, –5), (1, 3, -2,…

A: The given set,S=2,5,-3,-2, -2,-3,2,-5, 1,3,-2,2, -1,-5,3,5

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

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

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

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

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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 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 spanned by the given vectors. 3 Span 3 -1,2 1 3 4

A: The given subspace consist of all vectors in Span-231, 3-12, 123, -154. Take S=-231, 3-12, 123,…

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: 7. Find a basis for, as well as the dimension of the subspace of R* generated by the vectors (1, -1,…

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

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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: 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,…

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

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

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Q: Compute the projection of (1, 1, 1) onto the subspace generated by (0, 1, 0) and (-4, 1, 3)". Record…

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Q: Find a basis for the subspace of R* consisting of all vectors of the form (a, b, c, d) where c = a +…

A: To Find: Basis for the subspace of R2  of the form (a,b,c,d) such that c=a+7b and d=a-6b

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

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Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0,3), (2, 1, –2), (0, – 1,8), (7,2,…

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Q: Determine whether (1,1,1,1),(1,2,3,2),(2,5,6,4),(2,6,8,5) form a basis of R^4 (R). If not, find the…

A: Given set of vectors is  S=1, 1, 1, 1, 1, 2, 3, 2, 2, 5, 6, 4, 2, 6, 8, 5. We have to determine…

Q: Show that (4, 14, 8) lies in the subspace of R generated by (-1, 3, 1) and (4, 1, 2). (4, 14, 8) =…

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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,…

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Q: Find a basis for the following subspace: W₁ = span{[1, 0,-1, 2], [4, 1, -6, 7], [1, 2, -5, 0], [1,…

A: Given W1=span1,0,-1,2, 4,1,-6,7, 1,2,-5,0, 1,1,-3,1   To Find: A basis for the given subspace.

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

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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 of the following subspace of R*. span {(-1, 2, 1, 0), (2, 0, 3, –1), (4, 4, 11, –3),…

A: Given span−1,2,1,0,2,0,3,−1,4,4,11,−3,3,−2,2,−1 We have to find the basis of the space…

Q: Find a basis for the subspace W of Rª orthogonal to {(1, –2, 3, 4), (3, –5, 7,8)}. Find a basis for…

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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: The set of all nxn matrices having trace equal to zero. is a subspace W of Mnxn(F). Find a basis for…

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Q: determine whether the first vector is in the subspace of R3 generated by the other vectors. 1) (1,…

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

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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.