(9.) Show that W is not a subspace of V where W consists of all matrices A for which A² = A.

Q: Let V be the vector space of real 2 × 2 matrices with inner product (A|B) = tr(BtA). Let U be the…

A: Now , V=abcd:a,b,c,d ∈IRbe the Vector spaceof 2×2 real matricesendowed with the inner…

Q: 2b Let W = { "] | a, b e R}. a. Find a basis for W. (Your work here proves that W is a subspace of…

A: Given below the detailed solution

Q: Let V be the vector space of all (3×3) matrices and W be the set of all (3×3) matrices A for which…

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Q: Consider the 2 X 2 matrices A1 =  1      1           A2 =  0      1        A3  =   0      0      A4…

A: Thus, the four matrices are not linearly independent.

Q: Let V be the vector space of real 2 × 2 matrices with inner product  (A|B) = tr(B tA).  Let U be the…

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Q: If S is a subspace of R", then so is the orthogonal complement of S.

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Q: Let S be the set of matrices of the form a -a :). -b b where a and be R. The vector addition and…

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Q: Find a basis and state its dimension for the following subspace in Rª 3r+ 6s-t 6r-28-2t -9r+ 5s + 3t…

A: Given that 3r+6s-t6r-2s-2t-9r+5s+3t-3r+t: where r,s,t∈ℝ

Q: Let V be the vector space of real 2 × 2 matrices with inner product    (A|B) = tr(BtA).    Let U…

A: Let A∈skewsymm2 and B∈symm2 Then  A,B=trBtA=trAtB , since A,B=B,A=tr-AB=-trBA=-trBtA ,since B∈symm2…

Q: Let W be the subspace spanned by the given vectors. Find a basis for W-. 1 -1 1 W1 W2 -5 -2 1

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Q: What is the dimension of the following subspace U of R2x2 ? 3 U = span({ }) -2 -2

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Q: d) If A and B are 4 x 4 nonsingular matrices such that |2A¬'B²| = 32, then |4| = 8 e) Let S =…

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

Q: 20) Let W be the vector space of all symmetric 2 x 2 matrices. Show that W sisomorphic to R³

A: Introduction: The set of vectors v1, v2, ..., vn in V is said to be linearly independent if the only…

Q: Let W be the subspace of R4 defined by the equation x₁ - x₂ + 2x3 + 4x4 = 0. Find a linear…

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

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Q: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

Q: 26 Let V be the vector space of all 2 x 2 matrices and let W be the set of matrices of the form X -x…

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Q: Determine whether the set U consisting of all matrices of the form X 2x is a subspace M22-

A: The given set U=x02xy| x,y∈ℝ. We have check whether the set is a subspace or not.

Q: how that if T is a linear operator on V and W1, W2 are T-invariant subspaces of V, en W1+ W2 is a…

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Q: If W is a subspace of ℝ4 whose dimension is 2 then is any set of 2 vector is a basis for W

A: Answer

Q: Determine whether the vectors w₁ = [2,1,–3], w₁ = [4,0,2], and w3 = [2,-1,3] form a basis for the…

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Let W be subspace spanned by u's. Here , u1 = 1101 , u2 = -131-2 , u3 = -1011 Also , y = 644-1 We…

Q: (b) Define subspace and Verify whether is subspace v = {(x,y,2):x,y,2ER² and x-2y+3z = 5}

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Q: 3 Let M₂(R) be the vector space of all 2 × 2 matrices with entries from R. Show that M₂ (R) = W₁ W₂,…

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