Let M22 be the vector space of all real 2 × 2 matrices. Consider the subset W = {A ∈ M22 ∶ A is an orthogonal matirx} Prove or disprove that W is a subspace of M22. [Hint: A is an orthogonal matrix if ATA = I ]

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Q: 1. Let M22 be the vector space of all real 2 × 2 matrices. Consider W= D = 2} be a subset of M22.…

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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

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A: First we calculate the basis of V.

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Q: 4. Let A be an m x n matrix and b a non-zero m × 1 matrix. Show that the set of all n x 1 (column)…

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Q: Find the dimension of the following vector spaces. (a) V = {0}: dim V = (b) V = R¹: dim V- (c) V is…

A: (.) Dimension: The number of vectors in a basis of a vector space  is called dimension of..(.)…

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

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Q: Find an explicit description of the null space of matrix A by listing vectors that span the null…

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

Q: Let A= {a1,a2,a3} and B= {b1,b2 b3} be bases for a vector space V, and suppose a, = 5b, - b2, a2 =…

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Q: Q2. Show that M2x2 , the set of all 2× 2 matrices is a vector space. Explain your answer? Good Luck!

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Q: Notations That Represent A Line

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Q: Suppose there exists a 2x2 diagonal matrix with a standard operation. Prove that this set is a…

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Q: If A and B aren × n matrices which are similar, then rank(A) = rank(B). O true O false

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A: We have to prove that every vector has unique representation.

Q: Find a formula for the dimension of the vector space of symmetric n X n matrices.

A: Given: symmetric  n×nmatrix