Suppose A is a 3x5 coefficient matrix of a homogeneous system and suppose that A has two pivots. What is the smallest possible dimension of the null space of A ? What is the largest possible dimension of the column space of A?

Q: Give an example of a 3 x 3 skew-symmetric matrix A that is not diagonal. A =

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Q: Suppose that A is a 18 x 7 matrix and the null space of A has dimension 3. What is the rank of A?

A: For a m×n matrix, the number of rows is equal to m and the number of column is equal to n .

Q: Suppose that A is a 4 x 8 matrix that has an echelon form with no zero rows. Find the dimension of…

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Q: If a square matrix A is not invertible, then the columns of A could be either linearly independent…

A: We know that if a matrix is invertible then its column are linearly independent. Column A is…

Q: A matrix A is said to be skew symmetric if AT = −A. Show that if a matrix is skew symmetric, then…

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Q: If S = A + iB is a Hermitian matrix, are its real and imaginary parts symmetric?

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Q: Prove that the main diagonal of a skew-symmetric matrix must consist entirely of zeros.

A: Given-Skew symmetric matrix. To prove- That the main diagonal of a skew-symmetric matrix must…

Q: If A is a nonsingular matrix, what is the null space of A?

A: Given the non singular n x n matrix A. The objective is to determine the null space W of A Then,…

Q: 3.11 Definition A square matrix is nonsingular if it is the matrix of coefficients of a homogeneous…

A: In the given problem the concept of rank of a matrix is used to obtained the cases for the existence…

Q: If the null space N(A) of a 5 xX 6 matrix A has dimension 4, what can you say about the dimension of…

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Q: A homogeneous linear system in n unknowns, whose corresponding augmented matrix is in Reduced Row…

A: Given that: A homogenous linear system with 'n' unknowns, and whose corresponding  augmented matrix…

Q: Let A be the reduced coefficient matrix of a homogeneous system of m linear equation in n unknowns.…

A: We need to find if the statement is true or not.

Q: 8.) If A is an mxn matrix, what are the largest possible value for its rank and the smallest…

A: As per the instruction, we will be answering only the first one. For (8), We have that A is an mxn…

Q: the null space, and the row space of the matrix A.

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Q: Give an example of a 3 x 3 upper triangular matrix A that is not diagonal. A =

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Q: Construct a matrix system Ax = b, who has a particular solution Xp |1 and the nullspace of the 3…

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Q: 32. Construct a nondiagonal 2 × 2 matrix that is diagonalizable but not invertible.

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Q: Suppose that A is a 3 × 9 matrix that has an echelon form with no zero rows. Find the dimension of…

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Q: In a matrix A, the dimension of the row space of A is equal to the dimension of the column space of…

A: The given statement is

Q: Find the column space of the 10 × 20 matrix A if the system Ax = b is solvable for every b. Justify…

A: Note that : Ax = b has a solution if b lie in column space of A.

Q: Find a fundamental matrix for the system = (; 3)* -2' x'(t) : 2 -2

A: x't=3-22-2x   Let A=3-22-2 Characteristic equation of A is given by  λ2-trAλ+detA=0 where trA is the…

Q: (1) A= BCB, where C is an n x n symmetric positive-definite and B is an n x n symmetric matrix;…

A: In part l, We are given that A=BCB Here, C is n×n symmetric positive-definite. So, xTCx>0 with…

Q: If the null space of a 9x5 matrix A is 2-dimensional, what is the dimension of the row space of A?…

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Q: Suppose A is a 5x7 matrix and nullity (A)=3, Then the dimension of the row space of A is IS

A: Given, A is 5*7 matrix and nullity(A) = 3 We have to find dimension of row space of A

Q: Suppose A is anmxn matrix whose columns are linearly independent. What is the nullity of A?

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Q: Suppose A is a 10x10 invertible matrix. Then A is row equivalent to the 10x10 identity matrix. A)…

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Q: Suppose that A is a 4 x 7 matrix that has an echelon form with one zero row. Find the dimension of…

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Q: If the rank of the coefficient matrix and the augment matrix of a linear system are same then which…

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Q: Find the column space of the 10 x 20 matrix A if the system Ax = b is solvable for every b. Justify…

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Q: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

A: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

Q: Let A be a 7 x 4 matrix. (a) What is the maximum possible dimension of the row space of A? - (b) If…

A: Given matrix A is 7×4. a) what is maximum possible dimension of the row space of A? b) If the…

Q: Prove that the nonzero rows of a matrix in a row echelon form are linearly independent

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Q: If the null space of a 7 x 6 matrix A is 5-dimensional, what is the dimension of the column space of…

A: We solve given problem with the help of rank nullity theorem

Q: If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

A: Given A is square matrix whos rows add up to zero vector.

Q: If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the row space of A?

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Q: Suppose A = QR is a QR factorization of an m × n matrix A (with linearly independent columns).…

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Q: Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear…

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Q: What is the rank of a 7x9 matrix whose null space is five dimensional? rank A =

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Q: How do the dimensions of the null space and column space of a matrix relate to the number of lead…

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Q: If A is a constant matrix, the fundamental matrix of the system x' (t) = Ax(t) is non-constant. True…

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Q: What is the maximum rank of a 5 X 3 matrix? What is the minimum rank of a 5 X 3 matrix?

A: Concept: A rectangular array of numbers (or other mathematical objects) for those the operations…

Q: a. The span of a set of vectors (v1, v2, ..., Vk) is equal to the column space of a matrix ... b. If…

A: Let us state whether the given statements related to Matrix and Vector space are True or False with…

Q: If a 4 by 5 matrix has null space of dimension 3, then its rank is: 3 2 4 1 5

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Q: Show that if a square matrix A has two equal columns, then A is not invertible.

A: since not a particular question asked ,as per guidelines solution to only first question (i.e Q1) is…

Q: Let A be a 4x4 singular matrix. What is the smallest possible dimension of Null Space of A? A) 2

A: Using,  Rank- Nullity Thereom

Q: Two augmented matrices for two linear systems in the variables x, y, and z are given below. The…

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Q: Suppose that A is a 7x8 matrix, and the dimension of the column space is 4. The dimension of the row…

A: A is 7×8(m×n,say) matrix . Given dimension of column space is 4.

Q: Find the (1,4)-entry of the reduced row echelon form of the following matrix:

A: Follow the procedure given below.

Q: Determine h such that; a) the system has a unique solution b) the system has no solution

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Q: a) In statistical theory, a common requirement is that a matrix be of full rank. That is, the rank…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

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.