15+ find the dimensions of the following vector spaces
A The vector space of all upper triangular 2 x 2 matrices b The vector space of all diagonal 5 x 5 matrices C The. To show that X is a vector space it suffices to show it is a subspace of R 6 5.
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A The vector space of 2 x 2 matrices with trace 0 b The vector space P3 x of polynomials with degree less than 3 c The vector space.
. Find the dimensions of the following vector spaces. A The vector space of all upper triangular 4x4 matrices b The vector space of all diagonal 5x5 matrices c The vector. How to find dimension of vector space.
Problem 15 Previous Problem List Next 1 point Find the dimensions of the following vector spaces a The vector space R6x4 b The vector space of 3 x 3matrices with trace 0 c. 1 point Find the dimensions of the following vector spaces. Answered 2021-12-04 Author has 15 answers Because a diagonal matrix will have only n entries in total so dimension of diagonal matrix will be equal to square of its no.
To show that X is vector space consider x 1 x 2 X and v V. A The vector space of all diagonal n x n matrices. Section 45 Now part a of Theorem 3 says that If S is a linearly independent set and if v is a vector inV that lies outside spanS then the set S vof all of the vectors in S in addition to v.
Expert solutions Question Find the dimension of each of the following vector spaces. Find the dimensions of the following vector spaces. B The vector space of all symmetric n x n.
But I dont know how. Whereas your people previous exercise 9 14 for a new matrix T. We know that x 1 v 0 and x 2 v 0 so α x 1 β x 2 v α x 1 v β x 2 v 0 so V ker α x 1 β x 2.
For α i R and A i X if v V A i v 0 and so i. So we use the three x 3 matrix with entries 3 -1 1 7 -5 1.
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