1. (a) Let U {A € M3 (R) | AT = -A}, a subspace of M3 (R). (i) Find a basis B for U. Justify your answer. (ii) Suppose that C = {C1, C2, C3} is another basis for U and that -5 -1 PB-C = 7 -8 -3 -4 3 1 Find C1. Justify your answer.

Q: 2. How many vectors does any basis of of Max(a+2)(R) contain, if a = max1<i<10 a;?

A: Since, dimension of a vector space is equal to number of elements in basis of vector space.

Q: 7. v₁ = (0, 0, 1), V2 (0, 0, 1), V₂ = (7, 4, 11), V3 = (5, 3, 13) 8. V₁ = V1 (2, 0, 0, 0), v₂ = (0,…

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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…

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Q: 13. Do the set of vectors S = { x²+2x-4, 6x² +7x+3, 2x²+x) a basis for P2? Refer to the definition…

A: The given set is;  S=(x2+2x-4, 6x2+7x+3,2x2+x).

Q: QUE d. 1x) 3.1. the change of basis matrix from B to C. 3.2. [x]c for x = 3b₁ + 4b₂ + b3. Let B =…

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Q: Let p₁ (t) = 7+t², P₂ (t)=t-2t², P3(t) = 2+t-4t². Complete parts (a) and (b) below. a. Use…

A: The polynomials p1t, p2t and p3t belongs to the vector space P2 because P2 contains all the…

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Q: 9) please be clear with your answer, thanks!

A: Given the coordinate matrix of x relative to a (nonstandard) basis B for Rn, find the coordinate…

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A: Given a 3×3 matrix. A=R1R2R3 where R1, R2 and R3 are the three rows with three columns, i.e. three…

Q: 5. Explain why three linearly independent vectors u,v,w in R³ form a basis for R³. (Hint: Consider…

A: Basis of a vector space :                               A non empty sub set S be a basis of a…

Q: Let R2x2 be a linear space with all 2 × 2 real matrices. (1) Find a basis of R22 and dim (R²x2); (2)…

A: Given  be a linear space with all  real matrices.Therefore .We need to find the basis of .The inner…

Q: Q.2) For VR2 and B = {(1,2), (3, 4)"}, C = {(7,3), (4,2)"}; consider one vector v = = (1,0) ¹. •…

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Q: 2. Find the change of basis matrix from B to B' and the change of basis matrix from B' to B.

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Q: Find the change of basis matrix from B₂ to B₁. B₁ = = -13/11 31/22 -12/11 -2 GUEROOD {}} B2 = 1 1…

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Q: The matrices [8]. A₂ = [] ^--^-i [] , A4 = form a basis for the linear space V = R 2x2. Write the…

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Q: 7. Show that 3-{(; ) ( ) ( )} -1 2 S = 2 1 6 9 is linearly dependent in M22. Write one of the…

A: According to our guidelines I solve only 1 question, so kindly request you to repost the remaining…

Q: X= 3 -2 0 0 + -2 1 1 0 1 2 S+ t 0 1 Find a Basis for Column B of this Matrix

A: The row space (Row B) of a matrix is the set of all possible linear combinations of its row vectors.…

Q: (iv) If A is a symmetric matrix then x-Ax is a positive definite quadratic form. (v) If A is an n xn…

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