(a) Find the orthogonal complement S+.

Q: and Find the matrix A of the orthogonal projection onto W. A =

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Q: Find the matrix A of the orthogonal projection onto the line L in R² that consists of all scalar…

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Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

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Q: Determine k so that the vectors (1, –1, k – 1), (2, k, –4), (0, 2, + k, – 8) in R³ linearly…

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Q: Show every vector a in R² can be written as a linear combination of and

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Q: Determine whether the following vectors are linearly independent in R3:

A: They will be linearly independent if  a(1, 1, 3) + b(0, 2, 1) = 0  results in trivial solution only…

Q: Determine whether the following vectors are linearly independent in R2:

A: According to the given information, it is required to determine whether the given vectors are…

Q: What is the basis and dimension of M3(R)?

A: Basis: For a vector space V, the set of linearly independent vectors that generate the whole vector…

Q: Find the vector projection of b = 6î + 3ĵ + 2k onto å = î – 2ĵ – 2k.

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Q: Find the coordinate vector [p(x)]B of p(x) = x² + 4x + 4 with respect to the basis B = {x³ + x – 2,…

A: According to the given information, it is required to find the coordinate vector.

Q: as a linear combination of x = 7 4 and y = -3 Express the vector u -2

A: NOTE: Refresh your page if you can't see any equations. . write both vectors x and y in the matrix…

Q: compute the vector v if the coordinate vector vS is given with respect to each ordered basis S for V

A: Given that, S=1-200,-1301,1000,0-110Also,vS=0102

Q: Show that if u and v are orthogonal, then || u * v || = || u || || v ||

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Q: 1) Interpolate (by hand) the data x = [-1,0,1] %3D y = [0,1,3] using a) the linear spline basis;

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Q: Find the vector x determined by the given coordinate vector (xlg and the given basis 8.

A: In this question, we have given the Basis set of vector space and the coordinate vector [X]B. By…

Q: ind the coordinate vector [x]g of x relative to the basis 1 B = X = -2

A: Coordinate vector of the given vector

Q: Find the vector x determined by the given coordinate vector [x]R and the given basis B. - 1 1 3 - 2…

A: To find  The vector X determined by the given coordinate vector [X]_B and the given basis B.

Q: Find all values of the scalar k for which th e two vectors are orthogonal.

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Q: Find x in R2 whose coordinate vector relative to the basis B is [x]B =

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Q: Find the value of k for which the vectors 2 1 2 and -3 5 k are orthogonal. k =

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Q: Q. If B = {e, = the usual basis R2. Determine its dual basis. ?? ده رده را( = (D, 1)} is

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Q: Find the orthogonal projection of y onto u. y = -3/5] - 4/5 /5 4/5 b) c) d) 2.

A: The formula to find the orthogonal projection of y onto u is: projuy=u→.y→u→2.u→ Here,…

Q: (2) Prove that if a + b and a – b are orthogonal, then a and b have the same magnitude.

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Q: Verify that it is orthogonal to both a and b. (a × b) · a = (a × b) · b = %3D

A: Given

Q: Use the vectors a = [-1,0,1], b = [1,-1,5], and č= [0,-1,-2] to prove that a(bxč) # (åxb)xč

A: The answer is given below:

Q: At what value of k are these vectors collinear?

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Q: Find the matrix A representing the reflection about the line L in R² which consists of all scalar…

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Q: Is it true that there is a basis for R^4 that consists of five vectors?

A: False. First I recall you what is the definition of basis. set B of vectors in a vector space V is…

Q: Find the cross product axb. 1+9k, b- 41-j+ 3k Verify that it is orthogonal to both a and b (a xb) (a…

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Q: snip

A: Given Orthogonally diagonalize A=abba,If b not equal to zero

Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

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Q: Find the vector x determined by the given coordinate vector [x]R and the given basis B. -4 [x] B% =…

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Q: Let z = 6. and y Find the vectori = 47 - 7j and its additive inverse.

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Q: Find the coordinate vector of a -2 with respect to the basis B %3D for R.

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Q: 3. 2 Find a non-zero vector in R* which is orthogonal to 1 and 2 1

A: Given vectors are 1234, 3121 and 2311. We have to find the non-zero vector in R4 which is orthogonal…

Q: Suppose A and B are both orthogonally diagonalizable and AB = BA. Explain why AB is also…

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Q: draw the vector -u+ 2v + 4w

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Q: Prove that, if A is similar to B, and B is diagonalizable, then A is diagonalizable.

A: Given that A is similar to B and B is diagonalizable.  To find A is diagonalizable.

Q: 1) Write v as a linear combination of the orthogonal basis V₁,...,V using dot products: V= |; V₁ =…

A: The given vectors are v=23, v1=45, v2=-54

Q: Find all values of c so that (2, 1, c) and (c – 1, 2, 2c) orthogonal. are

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Q: Find

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Q: Let p = (2, t) and q = (3,5). Find t such that p and q are orthogonal. (Give your answer in two…

A: We will use the property of orthogonality

Q: Determine whether the following vectors are linearly independent in R3:

A: Given vectors, Let us set up a homogeneous system of equations, The set S = { X, Y, Z } of vectors…

Q: Consider the basis 3 3 6. B = 1 4 2 3 ,then v is the vector 3 of R. If [v]B =

A: Basis of a vector space is the linearly independent set which spans the vector space.

Q: Let B = (1, x + 2, (* – 1)", 9x) be an ordered basis for Pg. Find the coordinate vector of f(æ) = 8a…

A: Answer

Q: Find the orthogonal projection of v=2 onto W.

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Q: Let TilPe > Pz , T (ax?+bx+c) = 2Qx+ b. Then the basis of NIT) is

A: Just use a definition of Nullity of transformation.

Q: Show that (u₁. U₂. u) is an orthogonal basis for R³. Then express x as a linear combination of the…

A: Answer is in next step. please give a like !!