[Step-by-Step] Let V be the set of all diagonal 2 * 2 matrices i.e. V=[cca 0 , 0 b] \mid a, b are real numbers with addition is defined as: A \oplus B=A B,
Question: Let \(V\) be the set of all diagonal \(2 \times 2\) matrices i.e. \(V=\left\{\left[\begin{array}{cc}a & 0 \\ 0 & b\end{array}\right] \mid a, b\right.\) are real numbers \(\}\) with addition is defined as: \(A \oplus B=A B\), and standard scalar multiplication. With these operations, is \(V\) a vector space? Justify your answer. If it is not a vector space, list all axioms that fail.
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(Solution Library) Let S=(1,0,-3,2),(0,1,2,-3),(1,-3,-8,7). Show
![[Step-by-Step] Let V=C[a, b] be a vector](/images/solutions/MC-solution-library-75169.jpg "[Step-by-Step] Let V=C[a, b] be a vector space and let S is a subset")
[Step-by-Step] Let V=C[a, b] be a vector space and let S is a subset
(Solution Library) Let S 1=(x, y) ∈ \Re^2 \mid y=x and S 2=(x,
![[Steps Shown] Let A be n x](/images/solutions/MC-solution-library-75171.jpg "[Steps Shown] Let A be n x n matrix. Prove that if A is invertible")
[Steps Shown] Let A be n x n matrix. Prove that if A is invertible
Solution: Let B= 1-3x^2+2x^3,x+2x^2-3x^3,1-3x-8x^2+7x^3,2+x-5x^2+5x^3
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