The sets B={[1 2 2 1]T;  [1 0 2 0]T;  [2 0 4 -3]T} and B'={[0 2 0 1]T;  [2 1 4 -1]T;  [1 2 2n 4]T} are bases for the same subspace of R4. Find the matrix M that translates B' coordinates to B coordinates.

Q: Let W be the subspace of IRª spanned by the vectors 4 2 and -1 Find the matrix A of the orthogonal…

A: Consider the given information: Let W be the subspace of ℝ4 spanned by vectors :1-11-1,4-2-1-7 To…

Q: Show that the solution set to a system of equations of the form a + a, x = 0 + an x = 0 a m, + ... +…

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Q: 1

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Q: What is the dimension of the subspace or the space of 5 x 5 matrices (ai) sucn that a11 +...+ az5 =…

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Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

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

Q: Suppose A is 10 by 10 and A2 = 0 (zero matrix). So A multiplies each column of A to give the zero…

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Q: a. . Is the set of vectors of the form a subspace of R³? Show your proof. La+2b

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Q: Find the closest point to y in the subspace W spanned by u, and uz. 17 1 2 %3D u1 = 0 |, u2 = - 1 2…

A: To find The closest point to y in the subspace w spanned by u1 and u2

Q: 1 Q5. Find an orthonormal basis of the subspace spanned by the vectors

A: The solution is given as

Q: Find a basis for the subspace of R3 spanned by S.S = {(4, 4, 8), (1, 1, 2), (1, 1, 1)}

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Q: Find an orthogonal basis for the subspace {(x, y, z) E R³ | x + 4y – 2z = 0} -

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Q: Find the subspace spanned by the three vectors [2 3 1]T, [2 1-5]T, and [2 4 4]T Feuth

A: We will check the  vectors that it is linearly dependent or linearly independent.  If the vectors…

Q: Which of the following sets is NOT subspace of IR? 2 Span -5 {8} Г1 2 31 The set of solutions to the…

A: solve the following

Q: Find a basis for the subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]). Show your work, and…

A: We find basis of subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]).

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

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Q: a Is the set of vectors of the form a subspace of R³? Show your proof. La+2b

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Q: Find the dimension of the subspace spanned by the given vectors.

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Q: a. Is the set of vectors of the form a subspace of R3? Show your proof. La+2b|

A: Since you have asked multiple questions, we will solve the First Question for you. If youwant any…

Q: Find the distance from the vector -1 y = -5 10 to the subspace W spanned by -2 1 u 0 and v= 2 ||

A: The given vector is y=-1-510 and the subspace is u=-200, v=12-1.

Q: Find a basis for the subspace given by the plane −3x + 2 y + 5z = 0.

A: Given that, -3x+2y+5z=0

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: Let A be a 80 x 90 matrix (80 rows and 90 columns). Does the homogeneous 0 always has nonzero…

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Q: Find a basis and dimension of the subspace described as follows:{(x, y, z, w) |2x + 5y – z=0} (0-0)…

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Q: 2. Is the set of vectors of the form a b a+2b a subspace of R³? Show your proof.

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Q: Find a basis for the solution subspace Ax=0 where A=[-2,4; 1,-2] OA. {(1,0),(0,1)} O B. {(1,2)} C.…

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Q: Next Find a basis of the subspace of R° spanned by the following vectors: -1 -5 3 -4 -4 -1 2 -4 3. 7…

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Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

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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),…

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Q: In C[−π, π], find the dimension of the subspace spanned by 1, cos 2x, cos2 x.

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Q: determine the dimension of the subspace of R3 spanned by the given vectors.

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Q: Find a basis for the subspace given by the plane −3x + 2y + 5z = 0.

A: we have to find a basis for the subspace given by −3x +2y + 5z = 0.

Q: ) Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: First we need to write given vectors in matrix form and try to use row reduced echelon form(RREF) :

Q: Find a basis for the subspace and state the dimension. p– 2q 2р-5r :P,q,r e R а. -2q +2r -Зр+ 6r| 1…

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Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12

A: To find  The closest point to V in the subspace spaneed by the given vectors.

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

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: 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: determine the dimension of the subspace of R3 spanned by the given vectors.

A: Determine the dimension of the subspace of ℝ3 spanned by the given vectors.

Q: Find the orthogonal projection ŷ of y = -5 onto the subspace 6. -2 W = Span { uį 4 3 u2 %3D -2 Ex:…

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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: Show that the solution set to a system of equations of the form au*, + Azyš, + + a, x = 0 Inn + ar =…

A: The given system of homogeneous linear equations is equivalent to a matrix equation of the form: Ax…

Q: 4. Find the distance from the vector j = to the subspace on R³ spanned by { 19: | }

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Q: Find a basis for the subspace spanned by the given vectors. What is the dimension of the 1 2 2 - 1…

A: We have to solve given problem:

Q: 2. Find a 3 x 4 matrix R for which the null space of R is spanned by the vectors -- -E 0. v = u =…

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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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.