(a) Let 1 -2 1 1 1 2 A = and B = 1 Find the matrices X and Y that satisfy the following matrix equations: AXB= A² AY (A+ BY)¯' = A (b) Let C be a 3 x 7 matrix. What can you say about the size of the matrix Z if you know that ZC is defined, but Z"+C is not.

Q: a) Prove the following: a+b a a a+b =b° (3a +b) a a a a+b

A: Since you have posted more than one question, we solve the first one for you. For the other…

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A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: find the inverse matrix

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A:

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A: here question has a mistake , though I correct it and solve it for you, here two different f(x) is…

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A:

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A:

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A:

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A:

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A:

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A: Let A be a mxn matrix, To Check and explain: whether the following statements are correct or not.…

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A:

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A: For the given matrices A, B, and C. We have to choose the correct option.

Q: 3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that…

A: Trace of matrices is sum of its  diagonal entries

Q: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

A:

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A: Initial investment is $500 and the money gets doubled in 3 years.

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A:

Q: Let b₁=(1). -(-9), --(-4), C1 = = (-3). {c₁, c2} be bases for R². Find the change of coordinates…

A:

Q: Rank of the matrix A = (a) 1 (b) 2 (c) 3 (d) 4 1234 6 7 8 765 2468 5 8 is,

A:

Q: Let 2 -1 A = 1 -1 0 2 Find an orthogonal matrix P and a diagonal matrix D such thatt D = P"AP. D =…

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Q: he matrix is Α = et result hitting · 230 1 -1 3 401 -1 Α Α ΑΑ

A: Topic:- matrix algebra

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A:

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A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

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A: The given statement is false.

Q: If A is a matrix that satisfies the following equation. Find: Trace(A-17I)^-1

A: Given,            A=pqrt-pq0082To find:  TraceA-17I-1

Q: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

A:

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A:

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A:

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.