[1 2 1 2 2] 10. Let A=2 2 1 0 1. 1 1 1 1 3| (a) Find the bases for Col A and Row space of A (b) Find the rank of A (c) Find the bases for Nul A (d) Find the dimension of the Nul A.

Q: Prove that if a is perpendicular to b, then |a +b|^2 = |a|^2 + |b|^2 .

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Q: Step Justification -(-v) + (-v) = 0 and v + (-v) = 0 ---Select--- --Select-- -(-v) + (-v) = v + (-v)…

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Q: Let (u, v) be the inner product on R² generated by A = [ 6 -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find <u, v>

Q: Niwl 까다 t~M-JJ-100 -100 F الى s A= w하다 아 아까 Nt site wit Nt s

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Q: 5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R³,…

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: Let ((u,,u2,U3),(V1,V2,V3))= 2u, V1 + 3u2V2+ U3V3 be an inner product on R. Determine ||(1, – 1, -…

A: Explanation of the answer is as follows

Q: Find the scalar triple product u.(v x w) if u = 3i - 2j - 5k; v = i + 4j - 4k; and w = 3j + 2k. And…

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Q: 6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find the .

Q: Let p (x) = ao + a¡x + a2x² and q (x) = bo + b1x + b2x² be vectors in P2 with inner product = aobo +…

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Q: Find Im(A) for A = O Im(A) span = Im(A) = span Im(A) = span Im(A) = span 1 2 3 2 3 5 3 347 3 . Then,…

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Q: Let V = R?. For (u1, u2), (v1, v2) e V and a e R define vector addition by (u1, u2) # (v1, v2) :=…

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Q: All computations must be shown. 1. Let pi(t) = 1+ t², p2(t) = t +t² and p3(t) = 1 + 2t + t² be…

A: Consider the provided question, given,p1t=1+t2p2t=t+t2and p3t=1+2t+t2

Q: The dot product of two vectors can be written in the form s+ 18 t. x1 x2 in R" is defined by * ·ý =…

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Q: Let ((u1,u2,U3),(V1.V2,V3))=2u1 V1 + 3U2V2+ U3V3 be an inner product on R3. Determine ((1, – 1, –…

A: Given problem is :

Q: 3 4. Let u =-3 and A= 1 1 Is u belongs to the plane in R' spanned by the -6 -2 -8 columns of A? Why…

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Q: Which of the following is true for an inner product (u, v)? (u+v, w) = (u+w, v) (u, v) = (v, u) (v,…

A: use the property of inner products.

Q: Prove Theorem .Let Q be an orthogonalmatrix. detQ=+-1

A: Given that, “Q” be an orthogonal matrix, So, QQT=I=QTQ…

Q: Find the projection of b onto the column space of A: H A = = Split b into p+q, with p in the column…

A: Given: A=1-10111, b=459. To find the projection of b onto column space of A.

Q: Use indicial notation to prove the following vector identity (Ả × B) · (Ĉ × D) – (Ã · C)(D · B) – (Ã…

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