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

Q: Assume that T is a linear transformation. T: Projects vectors in its domain onto the line y = 2/3 x.…

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Q: Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 0 0 -4 0 1 -1 01 1 0 0

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Q: (2) Let M₂×2 be the vector space of all 2X2 matrices, and defined T:M 2x2 (A)=A+AT. where A= a [cd]…

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

A: Introduction: The set of vectors v1, v2, ..., vn in V is said to be linearly independent if the only…

Q: 10. B =

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

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A: Answer :

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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: Q4 let V=M₂x₂ of the form [a of with standard matrix addition and multiplication form -space-

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A: Given that T projects vectors in its domain onto the line y=4x. The direction vector of the line…

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

A: Given: symmetric  n×nmatrix

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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.