6.6. Let A and B be unitarily equivalent n x n matrices. a) Prove that trace(A*A) = trace(B*B). b) Use a) to prove that n n ΣΑ Σ.. j,k=1 j,k=1 c) Use b) to prove that the matrices (i 1) 1 2 4 and 2 i are not unitarily equivalent.

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Q: 9*) Let J and K be the Jacobian matrices of the functions y; = f:(x1, 82,. and their inverse…

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Q: aj bị c1 adjA if A = |a2 b2 c2| is a non-singular matrix prove that A: detA аз b3 C3

A: Matrix A is a non-singular matrix. This means; det A ≠ 0    A =a1b1c1a2b2c2a3b3c3adj A…

Q: 5. Find the three by three matrix A such that [r – y] A. y for all r, y, z in R.

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Q: 1- nullspace af now equivalent to the for the 1 1- 2. C. that puy -2 B. assume matrix pand Let A

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Q: Let U be an orthogonal matrix. Prove that det(U) is either 1 or –1.

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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.