Find a basis for the orthogonal complement of the subspace of R* spanned by the vectors. V1= (1, 3, -3, 5), v2 = (3,8, 1, 2), v3 = (1, 2, 7, -8) The basis for the row space is W1 = ( 1, 0 ) w2 = ( 0, 1 )

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A: a) Suppose that    be  a  basis  of      Then, which is  a  contradiction.    Hence, is  not a…

Q: Find a basis for the solution space of the given homogeneous linear system. X4- 3x2 + 2x3 - 3x4 = 0…

A: To find a basis for the solution space of the given homogeneous system

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

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Q: Let Hspan {(-3,-1,-2), (17, -1, 10), (-5, 0, -3)}. A basis for the subspace HCR³ is { vector

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Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 1, O),…

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Q: Find a basis for the orthogonal complement of the subspace of Rª spanned by the following vectors.…

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Q: Find a basis for the subspace of R3 spanned by

A: In this question, we find the basis for the span of subspace S. S={(-1,2,5),(3,03), (5,1,8)}

Q: Find a basis for the subspace of R'consists of all vectors of the form (a, 2a + b, b, 0). State its…

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Q: find an orthogonal basis and then an othnormal basis for the subspace U of R3 spanned by v1 =…

A: The objective of this question is to find an orthogonal basis and then an orthonormal basis for the…

Q: Find a basis for the subspace of R³ that is spanned by the vectors V₁ = (1,0,0), v₂ = (1, 1, 0), v3…

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

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Q: Let H = span {(16, -21, -14), (-17, 20, 13), (-23, 28, 18)}. }. vector A basis for the subspace HC…

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Q: Let V be the subspace of P^4 spanned by B = {1,x^2,x^4}. Create a chnage of basis matrix Cd,b if D =…

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Q: Basis Find a basis for the space of 2 x 2 lower triangular matrices.

A: In this question, we have to find the basis for the space of 2×2 lower triangular matrices. We know…

Q: (a) Find orthonormal vectors 91, 92, 93 such that 91, 92 span the column space of 1 2 1 A - 1 -2 4…

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Q: P₁1 = P₂1 = P31 = P1 = P2 = What is the matrix P = (P; ;) for the projection of a vector b E R³ onto…

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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 orthogonal complement of the subspace of R spanned by the vectors. v1 = (1,5,…

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Q: Let v1=[-2,2,1], v2=[-8,7,4], v3=[-29,25,14], w=[6,6,1] is W in {v1,v2,v3}? how many vectors are…

A: a) Given that v1=-2,2,1,v2=-8,7,4,v3=-29,25,14,w=6,6,1. It is required to find whether w is in…

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.