Find the bases af ths four fundamental Sudspores of the matria A | 3 4 09 NCA)- basis NCAT) = R CAT)-bais

Q: {C}.F]E])} 0 3 5 8 Let S = Span 2 a) List at least five vectors which are in S. 3 b) Is v= -7 in S?…

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Q: Let W be a space with an orthogonal basis given by and the shortest distance from W to y. Note: To…

A: Given that w=1-10011,111100.001-1-11y=-44431-4closest vector y to W is…

Q: Consider two numerical vectors named vecA and vecB with the same length. What does the vecA>vecB…

A: Let us find what the numerical vectors vecA>vecB yield in the next step.

Q: Let the ordeced two bases of the spaces B be A=- (1,3) (E),L)} and B=fF3,2).(5,1)} ln the case, find…

A: We required to find the transition matrix from base B to base A Which is given follow

Q: consider the Follobaly Bこ C-1リ-リ,23,2 C: ch) Cースリ a) Find the Change of baser Matta 6) C to B ?

A: Given : B=-1,-1,3,2 , C=1,1,-2,-1 First we write basis elements of B as linear combination of…

Q: Theorem 23. If u, v E Q then we can find integers a, b, d with d > 0 such that u = a and v = d'…

A: By Division Algorithm we know that,               Let a, b be two integers with b>0. Then there…

Q: 14. Prove the identity u v = %3Dl||u+ v|| -||u– v|| for vectors in R". *COD VDICTIT

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Q: O Given Basis tunchiono Xn- X and scalar prodnct <ti9)= foga) da ure Gram- Schmi dt precedue t find…

A: The given sequence of functions are: xn=xn The first four functions are: x1=x1, x2=x2, x3=x3 and…

Q: 1- Let V= IR" with multiplication . Then cheek t formai amat vector or mot? usuall addition & 8calar…

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Q: 2. Let V and W be vector spaces and let TE L(V, W). (a) Suppose V is finite-dimesnional, m is a…

A: a) Given that T is a linear transformation from V to W. w1,w2...,wn is a basis for range of T. Since…

Q: as the sum of two orthogonal orthogonal to ư

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Q: ⒸV-R² of α₁ [:] , *₁ [i] · <= [-] V=R²³² at = L₂= L3= let it be. Show that {2₁, 22, 23 } in V is a…

A: Given vectors are α1=101, α2=011, α3=1-12 The vectors α1, α2, α3 in V is basis, if  the matrix form…

Q: 4 - Consider the basis B = uj = U2 = U3 = of R3, and consider the vector v = Determine the…

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Q: Suppose that B = -2 -# are [ulc 3 11 14 COG)-GGH 17 and C= 3 2 6 4 5 find the coordinates of u with…

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Q: Compute the 4-volume of the parallelotope induced by the following four vectors: 3 3 -3 3 4 volume…

A: NOTE: Refresh your page if you can't see any equations. . write all 4 vectors in the matrix A find…

Q: 5) There is only one or thonormal basis for any vector space. A) True B) False

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Q: ould you please help me answer this question: Show that each of the following are not inner products…

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Q: 3) What is the rank of the set of vectors A1 , A2 and Az given by 25 5 A2 = l12] 64 8 %3D [144]

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: ,M= N = Which of the sets form K= L = a basis for R^2? O A) K, M and N OB) K and M OC) K only OD) K…

A: In this question we have to find which of the sets from a basis for R^2

Q: Gegee die vektore {v1, v2,..., Vn} in die vektorruimte R". As dit bekend is dat Given the vectors…

A: According to the given information it is required to explain about what we can say about the vectors…

Q: Let TiPe s Pe, T(ax?+ bx+c) = 2Qx+ b. Then the basis of NIT)

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Q: Let 2 4 -2 1 A = -2 -5 7 3 3 7 -8 6 3 a) Let w = -2 Determine if w is in Col A. Is w in Nul A? 3 b)…

A: Since you have asked a question with multiple subparts, we will solve the first three subpart…

Q: If x, y are two no vectors, then prove that |xty | || X lle y llq by = + // use Holder inequality.

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Q: Let weight vector a = j i is equivalent to a) >0 az aly ai aj b) >0 c) ay-ay> 0 d) ay-ay 0 for all

A: Solution :-

Q: Find the "unit vector" for (3, 8)

A: The magnitude of a unit vector is 1 .

Q: What is the size of the space stretched by the vectors {(1,0,2,0,1),(2,1,4,1,2),(1,1,2,1,1)}?    a)…

A: Given: (1,0,2,0,1),(2,1,4,1,2),(1,1,2,1,1)

Q: Let W = Span in W+ (the orthogonal complement to W)?

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Q: 18. Find the vector u in 2-space of length 2 that makes an angle 0 4.

A: A vector having length u→ and makes an angle θ is given by  u→ = u→cosθ i^ + u→sinθ j^

Q: -) V = [V₁, V², V3, ₁] = is и 21 21 30 Io 11 02 O u= [ ] linear combination of V or sto 9

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Q: Apply the Coram - Sahmidt or thomaratizatia trans form to given baris for R into an basis Uie the…

A: The given basis is B={(0,0,7),(0,1,1),(1,1,1)} We have to find the orthonormal basis of the given…

Q: a) Express the Hadamard gate in the form H = e AXBXC i.e. specify a, A, B, C with ABC = 1. b)…

A: A quantum logic gate (or simply quantum gate) is a fundamental quantum circuit that uses a few…

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.