Find all values of h such that the vectors {a,, a,, a,} span R, where a2 a3

Q: Find the vector z, given that u = (3, -2, 5), v = (0, 2, 1), and w = Z= z = −u + 4v + 1 _W 2 (-6,…

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Q: Find the norm of and the unit vector ū in the direction of T if 5 3 = ||7| = 5, ||

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Q: Find all values of h such that the vectors (a,, a,, a‚} span R°, where a a2 = 14

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Q: Find the value of k such that vectors x

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Q: b) Prove that if b e R" is any vector, then b . X +b.a.

A: I have given the proof by using only definition of convergence of sequence

Q: Let A and B be nonzero vectors. Find k e R such that A – kB is orthogonal to A + B.

A: We know if a vector P→ is orthogonal to another vector Q→ then scalar product (dot product) is zero.…

Q: Show whether R³ of the set B is a base and find the coordinate vector of the vector u = (- 1, -5,9).

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Q: Given vectors vi = |2 and v2 = 3 V1, Vị and v3 is linearly independent. find a vector v3 in R so…

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Q: Let DE be the vector with initial point D(8, 6) and terminal point E(-1, 5). Write DE as a linear…

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Q: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T in the 3D space, figure out c) e1 × e3

A: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T to Find e1 × e3

Q: Determine whether the vectors u = (2, –1,3), v = (4,1,2), and w = (8, – 1,8) span R³. If not find…

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Q: Three vectors u, v, and w exist such that - + = 0. Determine the value of ū+uw + (-). w, given that…

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Q: Choose the linearly dependent vectors in R Select one: a. O b. C. d. 1 2. 3.

A: Topic- vectors & matrix

Q: Let W be the set of all vectors of the form E 11 [3a +56 [T -a Find vectors and in R³ such that W =…

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Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

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Q: Find all values of h such that the vectors {a,, az} span R?, where a1 a2

A: Given that,

Q: For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax…

A: Correct last vector coordinates representation

Q: Find all values of b such that the set of vectors {(1, 1,0), (b, 1,0), (0, 2, 3)} is NOT independent…

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Q: Choose the linearly dependent vectors in R Select one: a. b. С. 2. d.

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Q: a. Consider the following vectors in R3 V1 = Vi = |2|,v3 1 Is the set consisting of these vectors…

A: Let's find.

Q: Consider two linearly independent vectors a = b 1 (а) (b) compute ||a – b|| find the vectors c E…

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Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: 2. Let Ā and B be nonzero vectors. Find k e R such that B – kĀ is orthogonal to Ā – B.

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Q: Show that if the vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

A: Given: The vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

Q: Use the triple scalar product to find the value of p that makes the three vectors below coplanar.…

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Q: Find all values of h such that the vectors (a,, a2, a3} span R, where h 12 a1 a2 a3 21

A: Given vectors are a1=247, a2=h1221 and a3=125. We have to find the all value of h such that vectors…

Q: Let ā, b, č and y be the three dimensional vectors a = j+2k, 6= -5i+ 2j+2k, č= 31– 5, j = i-7)…

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Q: Find the value of u that make the set of vectors {a, b, c, d} linearly dependent. [1 2 1 1] b = [0 1…

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Q: If a and b are unit vectors in R', show that ||a x b||? + (a · b)² = 1. %3D

A: On solving this we will get:-

Q: Let a, b, c and y be the three dimensional vectors à = 3j+4k, b=i+6j+2k, č=4i-8j, ÿ=−i+ Perform the…

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Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: Let u, v, and w be vectors in R". If u • v and u•w are both nonzero then v and w are not orthogonal.

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Q: Find all values of b such that the set of vectors {(1, 1,0), (b, 1,0), (0, 2, 3)} is NOT independent…

A: The given set of vectors:  110 , b10 , 023

Q: За + 2b Let W be the set of all vectors of the form Find vectors u and i in R' such that W = span…

A: We need to find the vectors u→ and v→ such that W=span{u→, v→}

Q: Determine whether the vectors ?→ = (2,−1,3), ? → = (1,1,−2), and ? → = (3,−1,5) span ℝ?. If not find…

A: Span: Let us consider the set of  vectors S={v1,v2,v3,......vn} in a vector space V is said to be…

Q: Find all values of h such that the vectors (a,, a, a3} span R, where a1 a2 a3 15

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Q: Prove that A.B + |A x B| < 2|A||B| for arbitrary vectors A, B and C.

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Q: Choose the linearly dependent vectors in R'. Select one: а. O b. O d. -2

A: The solution is given below

Q: Find all values of a and b (if any) so that the given vectors form an orthogonal set. (If an answer…

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Q: 7 Part (b) For each vector q and r, determine if the vector is in the span of the vectors w,, W,,…

A: Given vectors are  w1=1-124w2=230-2, w3=3-516, w4=1630 q=-893-4,r= -76-87

Q: Let u, v, and x be the following vectors in R’. *目…日。因 2 u = 1 X = 6 4 Let W = span{u, v}. Find the…

A: See the attachment. Send your feedback please.

Q: Find the norm of v, and a unit vector that is oppositely directed to v. (a) v = (3, 3)

A: The given vector is v = 3, 3

Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

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Q: Choose the linearly deperndent vectors in R Select one: a. b. 1 ][5 -2 d.

A: Vectors are linear dependent if all constant are zero.

Q: snip

A: Assume that the set 123,  41-2,  ab3 is an orthogonal. This implies that, a, b, 3·1, 2,…

Q: a. u= b. u= Cum

A: SOLUTION-

Q: Let y = U = write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u.…

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Q: Find values of a e R such that the vectors (–11, a, 2) and (a, a?, a) are orthogonal O A. 0, 2, –2 О…

A: given,      two vectors -11,α,2 and α,α2,α are orthogonal.

Q: Let a. b, and c be three-dimensional vectors. Identify whether the expression a- (b x c) will result…

A: We can solve this as follows:

Q: Prove the property if a and b are vectors and m is a real number.m(a . b) = a . (mb)

A: Let a=a1, a2, a3   and  b=b1, b2, b3. This implies that,