Home work Q: Find the minimum pdynomial for the following matrices. Is A diagonali zable -2 2 -3 1- A = -6 2 - A = 3. 2 -2 <-2 -2

Q: 12. Circle all the matrix products that ARE possible a. A3x4 B4x3 b. A2x2 B2x2 С. A4x1 B1x1 D. A2x3…

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Q: Is the produ ct elementary. matri ces dalways OF two an swer. elementary ? Sustify your

A: The product of elementary matrices need not be an elementary matrix. Recall that any invertible…

Q: If A is an invertible matrix, explain why A and AT must have the same null space. Is this true if A…

A: If A is invertible matrix then it has trivial null space and a matrix is invertible iff AT is…

Q: Provide an example of an elementary matrix for each of the three types of row operations and clearly…

A: The three types of elementary row operations on a matrix : (1) Interchange two rows (2) Multiply…

Q: Is the following matrix diagonalizable?

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Q: If A is a 4 X 2 matrix, explain why the rows of A must be linearly dependent.

A: If A is a 4 x 2 matrix, then it has 4 rows and 2 columns. Each row can be thought of as a vector in…

Q: -4x – y – 6z = -39 -9x + 7y + 4z = 47 – 7x – 6y + z = -52

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Q: Q5) Check whether the following matrix is diagonalizable or not. 7 -3 A = -9 -2 3 18 -8,

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Q: Explain the rank of a matrix?

A: The rank of a matrix is defined as the maximum number of linearly independent column vectors in the…

Q: Given two nxn matrices A and B, what are the criteria for the matrices to be inverses?

A: Given the matrices A and B of order nxn.

Q: When two m x n matrices are said to be equal? Explain there Applicability?

A: Two mxn matrices are said to be equal if their corresponding elements are equal.

Q: Find the matrix A if 2e2t et e²t - et e2tet 2e2t - et 3e2t3et 3e2t-3et et-e2t et - e2t 3et - 2e²t

A: To determine the matrix A , firstly I have taken the derivative on both sides then putting t equal…

Q: Please don't provide handwritten solution ...

A: Please comment down for any doubt. I hope my answer helps you.

Q: Give an example of a real square matrix that does not have an LU decomposition. Explain carefully…

A: Please see the below picture for detailed solution.

Q: 4, 4, -7 -5 Compute 2(2A - 3B) if matrix A = and matrix B = %3D 3 - 4 2. 2(2A - 3B) = (Simplify your…

A: Multiply A by 2A=433-42A=2433-42A=866-8Multiply B by -3B=-7-52-4-3B=-3-7-52-4-3B=2115-612

Q: Give an example showing that the rank of the product of two matrices can be less than the rank of…

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Q: s this matrix in row-echelon form or reduced row-echelon form

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Q: Give an example of a 3 × 3 matrix with real inputs that is not similar to a matrix diagonal

A: A matrix is said to be a diagonalisable  if it is similar to a diagonal matrix. Therefore we need to…

Q: Find the least-squares line that best fits the data (2, 3), (3, 2), (5, 1), (6, 0).

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Q: If A is n x n matrix, invertible, and B is n × n. Then Col(BA) =Col(B) O True O False

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Q: Explain the process of determining a minor in a matrix?

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Q: IA - (34) and B- (-5 8 -2 (a) (AB) (b) BTAT 10. f -5 find

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Q: Explain the Definition of a Matrix?

A: To define a matrix.

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.