Af a, B are two vectors in an inner product space V(F) and a, be F then prove that Re (a, B) = || a + BI? -|| a – BIP.

Q: Let u and v be non-zero vectors in 3-space. Prove that u and v are perpendicular if and only if |u…

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Q: 4. For vectors v and ū in an inner product space V, prove that u´ projzu and i are orthogonal.

A: v

Q: 5. Find a vector æ € R³ such that ||Ax – || is minimal, where [1 1 -2] 1 and b:= 2 1 1

A: By least square approximation ,      To minimize Ax-b the vector x is given by,…

Q: 2 Let L be the line in R³ that consists of all scalar multiples of the vector . Find the orthogonal…

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Q: Let u, w, v₁, v2, and v3 be the vectors in R defined by -19 37 3 4 -8 -18 12 2 U= 0=0 w= 0= 26 8 u+…

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Q: 1. Let, p is the set of all vectors of the form: m,n, te R. 2n (a) Is p closed under vector…

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Q: E: Let z = 1+i and z'=i-1. 2) Are these two complex numbers independant in the complex vector space…

A: We have to check for  two complex numbers independant in the complex vector space C? For this we…

Q: Which of the following cannot be defined as an inner product between two vectors (x0, Yo) and (¤1,…

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Q: 7. Given that a,b and are three vectors whereas is a scalar such that axř=b+ã and a = 2. By using…

A: Vector triple product is used

Q: Let  W = { (a, b) : a and b are real numbers, a + b =1 } . For any (a, b) and (c, d) in W and…

A: W={(a,b): a and b are real numbers, a+b=1} Since every vector space is a group under addition. If W…

Q: 1 1 1 Let A 1 1 1 1 1 1 3/5 -7/5 is in null(A), or 4/5 Either show that the vector show that it is…

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Q: a) Any vector z ER" can be writ ten as a line ar combination of the stand ard basis vectors e1, e2;…

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Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) 1, (u, w) = :8, (v,…

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Q: (1,1,..., 1)T be the column vector consisting of all 1s. Prove 0. 3. Let a = that La

A: Given: Let a=(1,1,......1)T  Then objective is to prove  La=0

Q: E Let z = 1+ i and z'=i-1. 1) Are these two complex numbers independant in the real vector space C?

A: We checked two complex numbers independant in the real vector space C?

Q: C: Let A = (v₁,..., v4) be any list of 4 vectors in the vector space V. Let B = (v₁-V2, V₁-V3,…

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Q: 3.) Prove that the left singular vectors of A one the night singular vectors of A".

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Q: Given K= (-2,-1), L=(2,4), M= (-3,-1) and N= (1,4), Prove that KĽ and MN are equivalent by Showing…

A: Two vectors are Equivalent if they have same magnitude and direction.

Q: Is v = |1a vector in the span of S = }|2| Use Gaussian elimination to support your answer.

A: To check v=111 a vector in a span of S=123, 012, -201 or not.

Q: There are Euclidean vector spaces with dimension 0 < dim < 00 that have no orthonomal basis. O TRUE…

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Q: Let v1, V2, V3 and u be vectors in R". If u is orthogonal to each of v1, V2, and v3 then u is…

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Q: Show that the set of complex number C={x+iy|x and y are real, i2=-1} is a vector space. Verify each…

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Q: s an inner product space, where (a, 5) = 4 – 5i.

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Q: Prove the following relation in the vector triple product : Ax(BxC) + Bx(CxA)+Cx(A x B) = 0

A: The answer is given in handwritten form in the step-2 box. Please check it.

Q: If are arbitrary vectors in R2x2, then the mapping A = (A, B) || A|| = ||B| = [a11 a12] a21 a22 A =…

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Q: Vectors a and b are some vectors in a space with inner Euclidean product, and it is known that…

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Q: Show that the complex numbers 2 + 3i and 1 – 2i generate the vector space

A: Given complex numbers are z1=2+3i    and    z2 =1-2i and   given vector space  is   ℂ over ℝ

Q: Prove that if IS or thogonal to both WaXhen is orthe gonal to every it' vector 1> 1X

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Q: A C -³/4 - 1/4 9/8 - 1/4 - 1/4 AZ = O 1/8 1/4 Find the vector 7 such that. 2 O (note: DON'T USE…

A: Give that, A-1=-34-14098-1814-14-140 and Ax→=206 We have to find the value of x→