Let V be the vector space of n-square matrices over a ficld K. Show that W is a subspace of V if W consists of all matrices A= (a] that are (a) symmetric (A" = A or ay = ag), (b) (upper) triangular, (c) diagonal, (d) scalar. %3D

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Q: b] Let W be the set of all 2 × 2 matrices A = such that Az = 0, where z = ||. Is W subspace of M22?…

A: A set W of vector space V over field F is said to be subspace of vector space V if W is itself a…

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A: Use the properties of a subspace or definition of subspace. Assume that the condition is true and…

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Q: (b) Let V = M2x2(F), be the vector space of all 2 x 2 matrices over the real number field. Define W;…

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A: According to the given information, it is required to prove that:

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A: a. X =155-1 b. Y = 255-2

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Q: Hi, need help with this calc 3 question, thank you!

A: Here,

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A: Vector spaces

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Q: Find the orthogonal compliment of the subspace W of 2x2 upper triangular matrices in the vector…

A: Using standard inner product in the space of matrices.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.