Show that the set of all solutions to the equation Ax = 0, where   A = [1 2 3 -2 -1 0]         [1 2 2 -1 -2 1]        [2 4 5 -3 -2 0]   forms a vector subspace in R^6. Find three special solutions corresponding to different free columns.

Q: 1. Is W=set of upper triangular 3 x 3 matrices a subspace of V=all 3 x 3 matrices? Support your…

A: I have showed that any two vectors form W linear combination of these also lies on W

Q: Each of the given sets below is not a subspace because at least one of the 3 properties of being a…

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Q: If the system Ax = b is inconsistent, then b must have a component in which fundamental subspace of…

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Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

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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 orthogonal projection matrix on the subspace defined by the equation: 2х-у-3z-0.

A: a) Let v1 = [3,6,0] and v2 = [0,3,-1] be two vectors on the plane As we have 2(3)-6+3(0) = 6-6+0 =0…

Q: Express the vector (-1,5,-6) in R'as (2,0,7), (2,4,5) and (2,-12,13). linear combination of

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Q: Please define the four fundamental subspaces? Please have your answer types.

A: Suppose that A is a m -by- n matrix that maps vectors in R^n to vectors in R^m. The four fundamental…

Q: 5. Show that {(1,-1,2,-3), (1,1,2,0), (3,-1,6,-6)} and {(1,0,1,0), (0,2,0,3)} do not span the same…

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Q: 2. How can you build a subspace of a vector space V by using a single vector vEV

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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 subspace always contains the zero vector.

A: True Because of subspace is a nonempty set.

Q: Find the components of the vector whose initial point is (2, 2, 4) and terminal point at (0, 2, 0).

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Q: Find a basis of the subspace ofRª defined by the equation 7x1+9x2+ 6x3 + 5x4 = 0. Basis:

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Q: Show that no linearly independent set of vectors can contain the zero vector.

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Q: Give two examples of infinite dimension vector spaces.

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Q: what is the smallest subspace containing the vectors u, v and w? what is the span of a set of…

A: Span is the all possible linear combination

Q: Explain the term Vectors that Span a Subspace.

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Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

Q: The set of all 2X2 matrices with ones on it's main diagonal is a subspace of R2x2 . true or false

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Q: Find a linearly independent set of vectors that spans the same subspace of R* 4 as that spanned by…

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

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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 = {(-11, 6, 4, 8), (-6, 3, 2, 4), (-2, 1, 1, 2),…

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Q: Show that the solution vectors of a consistent non-homogeneous system of m equations in n unknowns…

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Q: Find an orthonormal basis for the subspace spanned by (0,1,2), (-1,0,1) and (-1,1,3).

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Q: Sketch all four subspaces associated to mat 1 2 A = 3 6

A: Respected student, By Bartleby guidelines we have solved all the four subspaces with the first…

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: The set of all nxn matrices A such that the linear system Ax = 0 has only trivial solutions are the…

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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: Explain why the set of vectors V vector subspace of R2 = {[+] -1} ist :x>0, y> -1 is NOT a

A: Given: set of vectors  V=xy:x≥0,y≥-1 Explain why the set of given vectors is not a vector subspace…

Q: The set of all nxn matrices whose entries are odd integers is a subspace of Mnn. Is it true or…

A: A subset of a vector space is a subspace if it is a vector space itself. First of all the space…

Q: Describe explicitly a linear transformation from V, (R) into V, (R) which has its range the subspace…

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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 the projection of the vector v onto the subspace S. -1 1 -1 S = span v = -1 |-2/3 -2/3 projs v…

A: To find the projection of the vector v onto the subspace S, where

Q: The set of all solutions of homogeneous system AX = 0, where A is a 4 × 3 matrix, is a subspace of…

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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: 6. The projection of 12 onto the subspace of R spanned by ĝ V2 and a, 1 equals: -6 1,

A: 1. Let S be a non-trivial subspace of a vector space V and assume that v is a vector in V that does…

Q: Find a basis for the subspace of R4 spanned by S. S = {(3, 9, -3, 53), (-5, 3, 5, -3), (8, -5, -8,…

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Q: There are four vectors (1,a,b,c), (1,1,1,1), (1,2,3,1), (3,4,5,3). If the vector space (subspace)…

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

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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: Show that Null Space of Ax = 0 is a subspace.

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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: 9. Is the set of vectors {(-2, 2, 0), (1, 1, 1), (8, -4, 2)} over R linearly dependent or…

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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: Why are [0,∞) and (0,∞) which are subspaces of the real number system with the usual topology not…

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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.