6. Let {u₁, µ2} be an orthogonal basis for R². Express à as a linear combination of the u's. U₁ = 2 -3 , U₂ = 6 1 X = 9

Q: "Write x as the sum of two vectors, one in Span (u,.u₂.3), and one in Span (U4). Assume that (u) is…

A: In this question , we will write the 'x' as linear combination of remaining vectors .

Q: Answer considering the matrix with the given vectors as its columns

A:

Q: Performs the following operations on the indicated system b) F1 9.516 + B98.516 =

A: F19.516+B98.516=1AB1.A16

Q: 2.2. Find all solutions of the vector equation XịVi +X2V2 + X3V3 = 0, (1,0,1)7. What conclusion can…

A:

Q: 5. Express u = (-4, 3, —2) using the unit vectors.

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Q: 4. (a) Let L be the line in R' spanned by the vector (1,1, 1, 1). Find a basis for the orthogonal…

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Q: Show that the vectors a, (1, 0, 0), a2 = (1, 1,0), a, = (1, 1, 1) form a basis of C'(C).

A:

Q: Let a= and b= Show that there are scalars s and t so that sa+tb=. s = ? t = ?

A: a=-5,0,-3 and b=4,0,2sa+tb=27,0,15

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: (и, из) for Find the coordinate vector of w relative to the basis S R². Let ui (5, –4), u2 = (3, 7),…

A: Solvig by au+bv=w

Q: Find the linearly independent solution of the equation y"+xy'+y=0 around the point x=1.

A: We will find out the required solution.

Q: 7. Let S = Show that span S = R' and find a basis for R' consisting of vectors from S.

A: Span of vector : Let us consider a vector space V then the set S is aid to be the span of V if the…

Q: The vectors v' 1 = (4,5,3), v 2 = (8, r, 6) and v’ 3 = (6,7,8) form a basis of R for any real value…

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Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

A:

Q: Find the change-of-coordinate matrix P from B to C and P from C to B for the bases B = {1,t,t^2} and…

A: Let U={u1,u2,⋯,un} and V={v1,v2,⋯,vn} are two bases of a vector space W.The identity map I:W→W…

Q: Find the matrix A' for T relative to the basis B'. T: R > R, Tх, у, z) %3D (у — z, х - z, х + у), В'…

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Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector 8x³ + 2x²7x - 9…

A:

Q: Suppose M is the set of all real column vectors in R' whose components are equal, then the basis for…

A: See the detailed solution below.

Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Find the coordinate vector of a = [*]B= -10-30- 2 with respect to the basis B = for R³.

A: Given: It is given that, x→=42-4 and B=152, 01-6, 001. To find: We have to find the coordinate…

Q: Apply Gram-Schmidt orthogonalization to the column vectors of A, a1 = (1, 1, 0)T ,a2 = (1, 0, 1)T ;…

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Q: 4.) Are vectors Linearly independent? 2 3

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Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.)…

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: (-9,6) Use matrices to reflect the vector the line y = x. ove

A: Topic:- algebra

Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

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Q: Find an orthonormal basis of the plane x₁ +4x2x3 = 0.

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Q: 17.) If S= [(2, 2, 0), (2,-2, 0), (0, 0, 2)], find the set T of vectors that are the normalizations…

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Q: Let a1, a2, a3, . .., an be real numbers. Prove that at least one of them is greater than the…

A: We prove it by contradiction.