3 Let M₂(R) be the vector space of all 2 × 2 matrices with entries from R. Show that M₂ (R) = W₁ W₂, where W₁ a {(" "); a,bER} and W₂ = {(J)ieder} R

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: 5.- Demonstrate whether the vectors of the following vector space are linearly dependent or linearly…

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Q: (a) Let A, B be n × n symmetric matrices such that XTAX = X™BX for all column vectors X e R". Show…

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Q: 3. Let vi - [1,-2,3], va -(-1,-4,5], and va [5,-1,3] be vectors in R'. a) Use determinant to show…

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Q: Let u be a vector in R" and A be an m × n matrix. If u is orthogonal to each row of A then u is in…

A: Since u is orthogonal to each row of A, it means u is in null space of A.

Q: 4 [1] 2. Is the vector 5 in the column space of matrix A = 1 0 -2 −4 4 4 5 3 -13]

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Q: 6. Let B be the following ordered basis for R?: в %3 {(1,—1), (2, -3)} . Find the coordinate vector…

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