-7 7 Given v = 7 -10 find the coordinates for v in the subspace W spanned by 1 -7 -4 -1 2 3 -2 1 U2 = 1 Из 5 u4 = -1 and ug = -1 16 -2 1 5 1 Note that u1, U2, Uz, U4 and ug are orthogonal. Uz+ Uz+ U4+ U5 CO

Q: 2.2. Find all solutions of the vector equation XịVi +X2V2 + X3V3 = 0, (1,0,1)7. What conclusion can…

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Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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Q: (a) (b) Any set of vectors containing the zero vector is linearly dependent. Any set of more than ʼn…

A: Let  be a sub set of  containing the zero vector               Then consider the following…

Q: Determine the values(s) of h, if any, for the which the set of vectors {a1.a2,a3} is a linearly…

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Q: { (1, 2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii)…

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

Q: Find the dimension of the subspace spanned by the given vectors below. 4 6. -5 8 -4 O 3 O 4

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4V1 +…

A: Given  T(v1,v2,v3) = (4v2-v1,4v1+5v2)Image of v is given by T(1,-2,-4) = (-9,-6) hence (a). the…

Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

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Q: Suppose the row echelon form of a system of equations is x−2y−9z == −10 y+2z == −1 Enter the…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4v, +…

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Q: If V1 = [1 4 0] and V2 = [ -2 0 8], then determine all possible 1x3 row vectors V3 such that the set…

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Q: Suppose U₁ = 0 U₁+ U₂ = Check All Parts 3 -8 U₂+ Find the coefficients of a nontrivial linear…

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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.