Explain the fact Every rank one matrix is one column times one row.

Q: Matrix Invorse civen : A-1 23 -76 B-1 = and Find : A?

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Q: The multiplication of two non-zero matrices could be a zero matrix. O True False

A:

Q: Find the LU factorization of the matrix A, where 3 -5 2 3 2 -2 A = -1 -6 1 -1 -4 1 2 1 2.

A: We know that A = L U where L is the lower triangular matrix and U is the upper triangular matrix.

Q: Write down the name of the matrix according to the definition... 19. A"-0 20. AA'=I

A:

Q: Find the rank of the matrix 2. 1. 4 -2 3 3 -7 3.

A:

Q: What do we mean by the transpose of a matrix?

A: Matrix is a set of number which are arranged in form of rows and columns. They have elements in them…

Q: Find the determination of matrix:- 1 B 2

A: Part (A) - Given matrix - A = 215-1031-24Determinant of matrix A - A =…

Q: Is it possible to find a matrix in row echelon form whose column (iv) space is the same as that of…

A: (iv) No , it is not possible to find a matrix in row echelon form whose column space is same as that…

Q: -1 1 1 -2. -2 8. -8

A:

Q: Explain row vector in a 1 x n matrix?

A: To analyze row vector in a 1 × n matrix.

Q: What do you mean by transpose of a matrix? Explain their properties?

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Q: Determine the order of the matrix. 2 5 -4-4 6 1A) 3 × 2 B) 2 × 3 C) 6 D) 3

A:

Q: Due to what property, applied to the matrices below, do we know that A + B is a matrix of the same…

A: Given- Due to what property, applied to the matrices below, do we know that A + B is a matrix of the…

Q: The dimension of the row-space of a matrix equals the number of rows of the matrix. Select one: O…

A:

Q: Find the size of the matrix. Determine if it is 9 6 3 1 39 6 1 9

A: Count the number of rows and columns

Q: Express as a single matrix.

A: Given,

Q: The product of a 5 ´ 3 matrix and a 3 ´ 5 matrix is

A: When we do matrix multiplication: The number of columns of the 1st matrix must equal the number of…

Q: Find the transpose of the matrix. 0 1 7 2 -1 2 8 5.

A: Given that  The matrix is  To find the transpose of the matrix is

Q: Describe how the rank of a matrix can be used to determine if a system of equations has one solution…

A: Describe how the rank of a matrix can be used to determine if a system of equations has one solution…

Q: Envision a 2 x 3 matrix.

A: Let A be the matrix with order 2×3, which represents 2 as number of rows and 3 as number of columns.

Q: Explain why interchanging two rows of an augmented matrix results in an augmented matrix that…

A: Given:

Q: Write a 4 x 6 matrix with distinct non-positive entries and find its transpose

A: Topic = Matrics

Q: Find the rank of the matrix -1 2 니 -2 6 3 -7 3.

A: To find  The rank of a given matrix.

Q: Explain the Main diagonal within a matrix ?

A: The main diagonal within a matrix consists of those elements which lie on the diagonal that runs…

Q: Explain why a matrix that does not have the same number of rows and columns cannot have a…

A: Let A be the matrix of order m × n If inverse exists, then AA-1 =A-1A = I Where I is the identity…

Q: Does Size of a product matrix in Matrix Multiplication matter? explain the suitable size?

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Q: True or false: Two columns of a matrix may be interchanged to form an equivalent matrix.

A: Known fact: Any elementary row transformation of matrix produces an equivalent matrix.

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

A:

Q: The product of a 2 ´ 3 matrix and a 3 ´ 2 matrix is

A: When we do multiplication: The number of columns of the 1st matrix must equal the number of rows…

Q: State the dimension of the matrix. 4 -4 0 -2 7 -3.

A:

Q: Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in…

A:

Q: State the dimension of the matrix.

A: The dimension of a matrix is the number of rows by the number of columns. For example is a matrix A…

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

A:

Q: If A is a 3 X 5 matrix, explain why the columns of A must be linearly dependent.

A: In A is a 3 X 5 matrix, explain why the columns of A must be linearly dependent. You have 5 column…

Q: Find the nullspace of the matrix

A: We have given the matrix;

Q: What is the reduced row echelon form of a matrix?

A: A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the…

Q: Let A be a 3 × 3 matrix and let b = 3a1 + a2 + 4a3 Will the system Ax = b be consistent? Explain.

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Q: How can we determine the cofactor for each element in a matrix?

A: Query- How can we determine the cofactor for each element in a matrix? Answer-  The first step…

Q: Matrix multiplication is always commutative? justify it.

A: Matrix multiplication is not always commutative.

Q: Determine whether the matrix is in reduced row-echelon form, or neither.

A: We have to find

Q: Find the LU factorization of the matrix A, where 3 -5 2 -2 A = -1 -6 1 -4 1 2 1 2. 2.

A: Given matrix is A=−23−5232−22−1−61−1−4121. We have to find the LU-factorization of the matrix A. By…

Q: 1 2 6 41 2 3 2 5 6 2 3 0

A:

Q: What is meant by Zero matrix?

A: It is known that a matrix whose all the elements are zero is known as null or zero matrix.Moreover,…

Q: Describe when the multiplication of two matrices is not defined.

A: Given, multiplication of two matrices

Q: Find the rank of matrix 1        3 0       -2 5       -1 -2       3

A:

Q: Give an example of a nonzero 3 x 3 diagonal matrix A. A =

A: Diagonal Matrix: In linear algebra, a diagonal matrix is a matrix in which the entries outside the…

Q: What is a column matrix?

A: Definition of column matrix – A vector which is represented with a list of number is called a column…

Q: State the dimension of the matrix.

A:

Q: matrix is not easy to do with just row operations, because the

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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.