The matrix A(4x3) = 3,-5,1 second row 1,1,1 third row -1,5,-2 fourth row 3,-7,8. Use the Gram-Schmidt process to find the orthogonal basis for the column space of A.

Q: Find a basis for R that includes the vectors (2, -1, 5) and (4, 5, -5) {(2, -1, 5), (4, 5, -5), )}

A: Idea is we try to find a vector which is not in the span of given two vectors now collection of…

Q: In P2, find the the standard basis C = {1,t,t²}. Then find the B-coordinate vector for − 4 + 10t −…

A: We know that  is a vector space consisting of the set of all the polynomials of degree lessthan or…

Q: Write the 3D Rotation Matrix that first rotates around the y-axis by 0, = 45° followed by a rotation…

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Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: Linear Algebra. Please write your answer clearly. Thanks.

A: A point 0,2,-15 is given which is relative to an orthonormal basis, 0,1,0,-35,0,45,45,0,35. The…

Q: Find the matrix A of the rotation about the z-axis through an angle of pi/2, counterclockwise as…

A: To get the matrix A for a rotation about the z-axis through an angle of pi/2 counterclockwise, we…

Q: Find the change of basis matrix from B1 to B2. B₁ = 3 -21 and ẞ2 = 3,-5, 2

A: We have to find the change of basis matrix β1

Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: In P,, find the change-of-coordinates matrix from the basis B= (1-2t+P,3-5t+41,1 B-coordinate vector…

A: Given B=1-2t+t2, 3-5t+4t2, 1+4t2. To find P2 that transforms B to C, where C=1,t,t2 PC←B=131-2-50144…

Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: 2. Diagonalize the matrix using normalized vectors. B= 3 1

A: Given,        B=1331

Q: Determine the orthogonal basis by calculating w1 = w2 - [(23,5)] - [(-9,-2)] and calculating w2 Now…

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Q: Multiply the matrix P = A(ATA)-¹AT by itself. Cancel to prove that P² = P. Explain why P(Pb) always…

A: Here the Matrix . For this matrix P, .

Q: Find the change-of-coordinates matrix from B to the standard basis in R". 2 -2 3 8 -2 7 8. Pa

A: Uf7ygth

Q: Find the linear combination 3s1 + 4s2 + 5s3 = b. Then write bas a matrix vector multiplication Sx,…

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Q: Describe the solution set, x= x₂ of x₁ + 4x2 - 7x3 = -6 in parametric vector form. Select the…

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Q: Oa + Ob+0c + 4d la + (-1) b+ (-2) c +4d Oa + 1b + (-2) c + 5d la + (-1) b+ (-2) c + 2d 2a + 1b+…

A: 1) Let Tabcd=0a+0b+0c+4d1a+(-1)b+(-2)c+4d0a+1b+(-2)c+5d1a+(-1)b+(-2)c+2d2a+1b+(-10)c+4d   To Find:…

Q: Find an orthogonal basis for the column space of the matrix 6 5 -8 -5 -2 -1 -4 A = -1 3 1 Then find…

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Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

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Q: Consider the ordered bases 3 = {(1,0), (1, 1)} and ß' = {(4,7), (–2,5)} for R². %3| (a) Find the…

A: The solution is given as

Q: Find the coordinate matrix of x in Rn relative to the basis B'. B' = {(8, 11, 0), (7, 0, 10), (1, 4,…

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Q: entries

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Q: find the standard matrix for the reflection of IR squared about the line that makes an angle of π/4…

A: Consider line that makes an angle of  with positive  axis.To illustrate the standard matrix for…

Q: Consider the following matrix: 1 2 3 0 -3 A-3 6 -9 09 -2 5-9 -29 Give a basis for each of im(A) and…

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