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

Q: Can you provide one image or figure of the hermitian matrix?

A:

Q: Show that the matrix is not diagonalizable.

A:

Q: (3) Show that the system of quaternions can be represented as a system of real matrices of size 4 x…

A: Let h, j, k denote the imaginary units of algebra of Quaternions. Then the typical quaternion is in…

Q: must be a non-invertible matrix.

A:

Q: what is a Hermitian matrix? does every Hermitian matrix has to be square matrices?

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

A: .

Q: Give an example of a matrix M where MMT and MTM are not equal matrices.

A:

Q: Let A be an 8 × 5 matrix of rank 3, and let b be anonzero vector in N(AT ). Show that the system Ax…

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Q: Let A be a 5x7 matrix, then the smallest possible dimension of Null(A) is:

A:

Q: Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

A: Consider a square matrix A=000123456 and B=140250360 Here, all the elements of first row of the…

Q: Show that the zero matrix is the only 3 × 3 matrix whose null space has dimension 3.

A: Given- A zero matrix of 3×3 order. To show- that the zero matrix is the only 3 × 3 matrix whose null…

Q: Create a matrix A with the given Characteristics Dimension 3x3, IAl = 7 %3D

A: Here we create a 3×3 matrix whose determinants is zero.

Q: Find an LU-factorization of the matrix A such that A = LU. %3D 6 4 -2 1 -2 3 2. -2

A: Explanation of the answer is as follows

Q: #16

A: Recall the following facts.

Q: Find an LU-factorization of the matrix.

A:

Q: If the null space of an 8 × 5 matrix A is 2-dimensional, what is the dimension of the row space of…

A:

Q: Show that any nX n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

A: To show that any n x n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

Q: Construct a 3 x3 nonzero matrix A such that the vector is a solution of Ax = 0. 1 LA =

A: x=-1-1  1 Now let A=abcdefghi be the required vector. Then, Ax=0⇒abcdefghi-1-1  1=000⇒-a-b+c-d-e+f…

Q: ГО 5 4 5 1 2 2 3] A = [1

A:

Q: If the nulI snace of a 30x17 matrix is 13-dimensional, find the rank of the matrix.

A: We have been given the matrix which is of 30 x 17 i.e it has 30 rows and 17 columns. And it is also…

Q: How can I find a matrix, given the basis of the null space of said matrix?

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Q: Can we use cofactor expansion in a 2x2 matrix?

A: Can we use cofactor expansion in a 2x2 matrix?

Q: If there is conformability what are the dimensions of the product matrix?

A: let's matrix A and matrix B has dimension as  m×n and n×p respectively then dimension of matrix…

Q: Write a second degree equation matrix and prove that it is in vector space?

A: To show: An example of a second-degree equation matrix which is in vector space.

Q: Ч. W is the set of all 2x2 upper triangular matrices in Mzx2 (IR).

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Q: Show that the matrix below does not have an LU-factorization.

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Q: If A is an m × n matrix of rank r, what are the dimensions of N(A) and N(AT )? Explain.

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

A:

Q: Suppose a 3x8 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Ans: Given a 3×8 matrix has a rank 3. We want to find the dimension of the null space, dimension of…

Q: Explain why the columns of an n×n matrix A span R^n when A is invertible.

A: Consider, a matrix A of order n, which is a invertible matrix.Since, the set of vectors

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

A:

Q: Suppose M is a (6x6) matrix such that the dimension of its column space is 5 .Then the rank of M is…

A:

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: Every matrix has a unique reduced echelon form. Is this true or false?

A: Given statement is “Every matrix has a unique reduced echelon form. Is this true or false?”

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?

A:

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

A: Let A be a 5×3 matrix So A is a system of 5 linear equations with 3 variables. By rank theorem,…

Q: Explain why the row vectors of a 4 × 3 matrix form a linearly dependent set. (Assume all matrix…

A: Given: The Matrix is 4 * 3 matrix

Q: What is the standard basis of a skew-symmetric matrix?

A: To give the standard basis of a skew-symmetric matrix.

Q: Describe the range and null space of any n × n nonsingular matrixand the n × n zero matrix.

A: According to the given information first it is required to calculate the range of n×n non-singular…

Q: # Show that diagonally dominated matrices are always invertible. Now, what is a diagonally dominated…

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Q: Find the number of 3x4 matrices in row echelon form, with entires from F = Z/2Z

A: To find the number of 3x4 matrices in row echelon form, with entries from F = Z/2Z.

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

A:

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: Must an upper triangular matrix be in row-reduced form?

A: A square matrix whose all elements below the main diagonal are zero,  is called an upper…

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

A:

Q: Is it true that the sum of invertible n x n matrices is invertible?

A: Given: The statement is : Is it true that the sum of invertible n x n matrices is invertible? It is…

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.