Consider the following vector subspace of R 3 : a).Find a base for W. b).Is the base you found for W in the previous item orthogonal? c).Find the orthogonal complement of W. d).Find an orthonormal basis for the orthogonal complement of W.

Q: 1 3 0 4 2 0 0 6. -2 1 0 1 0 0

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A: We have We have to find a basis B such that is diagonal

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Q: Q#5: If Bij = €ijkak, show that B is antisymmetirc. %3D

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Q: Determine whether or not the given vectors in R² form a basis for R². 6 - [8]/1/2 5 8 Do the given…

A: Let c1 v1 +c2 v2 =0.So 6c1 +5c2 =0 and 3c1  +8c2 =0.Solving these we get c1 =c2 =0.

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A: Given, A=2-7-54   We have to find basis B.

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A: Solution:

Q: A= {(1,2,1,0), (3,–4,5,6),(2,–1,3,3),(-2,6,–4,–6)}

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Q: Assume that A is row equivalent to B. Find bases for Nul A, Col A, and Row A. 11 5 -7 6 110 3 7 11 3…

A: Nul A={x∈ℝ5|Ax=0}AX=0⇒Bx=0Bx=0⇒x1+x2+3x4+7x5=0     ...(1)                 5x3-10x4+5x5 =0…