If the null space of a 7 x 6 matrix A is 5-dimensional, what is the dimension of the column space of A? Justify.

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 6 x 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT .

A: We are given that a 6x3 matrix A has rank 3. So, dim(Row A) = 3. We know that dim(A) = dim(Row A) +…

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

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Q: If a 6 x3 matrix A has rank 3, find nullity A, rank A, and rank AT. nullity A = rank A= rank AT=

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

A: We write the 3x3 lower triangular matrix which is not diagonal

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

A: From the given information:

Q: If a 3 x 4 matrix has 3 pivot columns, then its columns span R. True False

A: A 3×4 matrix have 3 rows and 4 columns, in each column has 3 elements. Given that matrix have 3…

Q: Find that whether the following matrix is singular or nonsingular. 8 0 -5,

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Q: 2. Suppose that A is a 64 × 17 matrix and that the rank of A is 11. What is the dimension of the…

A: The given matrix is A of size 64×17. Also the rank of A is 11. As we know that for any matrix of…

Q: Suppose a 4x6 matrix A has four pivot coloumns. Is Col A=R4 ? What is the dimension of Nul A? What…

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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: Suppose a 5 × 6 matrix A has four pivot columns. What is dim Nul A? Is Col A = ℝ4? Why or why not?

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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: 5. If the null space of a 4 x 7 matrix A (4 rows and 7 columns) has dimension 5, what is the…

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Q: Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Multiple :    Let  A be 5 × 4 matrix . We have given that , rankA = 3. We need to find , dimension…

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

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

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Q: If A is any 5 by 5 invertible matrix, then its column space is __ . Why?

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Q: • Is it possible for a 5 x 5 matrix to be invertible when its columns do not span R°? Why or why…

A: According to the Invertible matrix theorem, the matrix with n x n order cannot be invertible if its…

Q: If A is a 4 × 3 matrix, what is the largest possible dimension of the row space of A? If A is a 3 ×…

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Q: If the rows of an n X n matrix A are linearly inde­pendent as vectors in Rn, what is the rank of A?…

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Q: Suppose that A is a 5 x 5 matrix which has a null space of dimension 4. The rank of A is rank(A) =

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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…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

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

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Q: Suppose A is a 3x5 coefficient matrix of a homogeneous system and suppose that A has two pivots.…

A: Solution is given below

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 null space of a 7 × 6 matrix  is 5-dimensional, what is the dimension of the column space of…

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

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Q: The row space of a matrix equals its column space. O True O False

A: Let the matrix Amxn having m rows and n columns. If the matrix has rank r after reduced Echelon…

Q: The row space and the column space of a matrix A do not have the same dimension. O True O False

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Q: If A is 3 x 2 matrix and B is 2 x 3 matrix, then AB is always: a. Invertible matrix b. singular…

A: We know that rank ofAB is always less then or equal to min{rank(A), rank(B) }

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: If A is a 7 X 9 matrix with a 2 dimensional null space, what is the rank of A? Could a 6 X 9 matrix…

A: Given that A is a 7×9 matrix with a 2 dimensional null space. We have to find the rank of A. Since,…

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

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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: 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: Suppose A, B, and C are three non-zero square matrices such that AC = BC. Is it true that A = B? If…

A: Not true

Q: Suppose A is a 3 x 4 matrix. If we can successfully multiply A with the matrix B, then which of 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.