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: Define Square matrix?

A: A matrix is the arrangement of data in rows and columns.

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: What is the rank of the matrix?

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Q: of a matrix is the factorization of a given square matrix into two triangular matrices.

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Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

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Q: しt A and B be similar inrertiblo matricen Ghow that and B" are rimilar

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Q: 1. Consider the matrices A₁ 4 = ( 1 ) - 1 3 0 A₂ 42 = (3-2) ₁ 4₁ = ( 2² -2²), , A3 0 -2 These…

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Q: (1) True or False? Justify your answer. (a) Let A, B, and C be two square matrices of the same…

A: for given three matrices with same dimension  and  is invertible,Again as matrix multiplication is…

Q: Why does no 3 by 3 matrix have a nullspace that equals its column space?

A: To show why does no 3×3 matrix have a null space that equals its column space. We know the…

Q: 1 0 0 6 A 0 1 0 7 0 0 1 1 1 0 0* 0 1 1 0 0 0 0 1 В 1 0 0 4. 0 0 1 5 0 0 0 0 1 0 0 4. 0 0 1 5 0 0 0 0

A: A matrix is in reduced row-echelon form if the following holds: 1) All the leading elements are 1.…

Q: What is the multiplicative identity matrix?

A: According to the question, we have to define the multiplicative identity matrix. As the above…

Q: How do you know whether a matrix is invertible?

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Q: Explain the rank of a n*n non-singular matrix?

A: Consider Use the property of rank which states

Q: If A and B are m × n matrices such that Col(A) and Col(B) are isomorphic, then the RREF of both…

A: If two vector space is Isomorphic then the dimension of the vector space must be same. The dimension…

Q: Explain the mandatory conditions for the addition of two matrices?

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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: If matrix [A] is a 5x5 matrix and a matrix [Z] is obtained by the row operations of replacing Rowl…

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Q: If A and B are square matrices of the same size, is (A + B)2 = A2 + 2AB + B2?

A: In matrices, the commutative properties are not valid. That is order of the matrices multiplication…

Q: Find a non-zero 2 × 2 matrix A such that A2 = A =

A: We have to find a A matrix of 2x2 such that, A2  = 0000  So let suppose a matrix    Satisfy the…

Q: Q5 Let -1 7 A = 1 15 -2 (5a) Find a 3 x 3 matrix P and a diagonal matrix 0 0 D= such that A = PDP-1…

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A: Why it is not possible to find the cofactor of a 4x3 matrix?

Q: If a 6 x 6 matrix contains 19 zeros, show that there are 4 zeros which are all in distinct rows and…

A: A 6x6 matrix has 36 entries. Given if a 6x6 matrix contains 19 zeros, then to show that there are 4…

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.