If a 3 × 8 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT.

Q: a) If a 7 × 5 Matrix A has rank 2, find dim(Null A), dim (Row A) and rank AT

A: 1) Given  7×5 matrix  rank(A)=2 using rank nullity theorem we have rank A + null A= number of…

Q: If A is a 5 x 6 matrix and the sum A + B can be computed, what is the size of B?

A:

Q: Construct a 4x3 matrix A with rank 1. Select the correct choice and, if necessary, fill in the…

A: We construct a 4×3 matrix A with rank 1.

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: If A is an n×n matrix with Col A​ = Rn​, how many solutions will there be to Ax​=b​, for any b in…

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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: |a b X y m nl

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Q: Given a 2 by 2 matrix, how do i show that it is a linear combination of unitary matrices

A: See the attachment

Q: Find a 2x2 matrix that forms an angle of n/3 cadians with the matrix P -- (: 9) 2 0 0 2

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Q: If a 3 by 3 matrix has det A = -1 , find det(½A) and det(-A) and det(A2) and det (A-1 ).

A: Properties of Determinant →i detcA=cn.detA    where n is the order of square matrix .ii det…

Q: find an LU factorization of the given matrix.

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Q: Find an SVD of the matrix. – 6 -5 A = A=

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Q: If a matrix L is a 2X3 matrix and the matrix M is 4X3 matrix, then LxMT is an ____ by _____ matrix.…

A: Solution: Given:    L is a 2X3 matrix and                 M is 4X3 matrix

Q: We say that, a matrix M is skew-symmetric if it satisfies MT = -M. Show that if a 3 x 3 matrix M is…

A: Skew-symmetric Matrix: A matrix M is skew-symmetric if it satisfies MT=-M where MTis the transpose…

Q: 3. If A, B and C are matrices with orders, 3 X 3, 2 X 3 and 4 X 2, respectively, which of the…

A: Note: There are many subparts in the question. So I will answer the first three subparts.…

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: Find the range of a (2 × 3) matrix B with rank(B) = 2

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Q: If a 4x5 matrix A has rank 4, find nullity A, rank A, and rank A". nulity A-[ rank A- rank AT-O

A: We have to solve given problem:

Q: Find a matrix B in reduced row echelon form that is rowequivalent to A, using elementary matrices.

A: Given- 2-40013006 To find- Find a matrix B in reduced row echelon form that is row equivalent to A,…

Q: a) If a n x (n + 5) matrix has rank n, find dim Nul A, dim row A and rank A". where n=9.

A: Explanation of the solution is given below...

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: 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: if A is m xN matrix pivot in every row, then Ax-b has that has a a unique solution for each b in Rm

A: The given question can be solved as shown in step2.

Q: 2) If IAI = 3, where A is a 3x3 matrix, caleulate the folowing: 2a) det ( ZA) 26) det (A) 2c) det (…

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Q: If A is a 2 x 3 matrix and the sum A + B can be computed, what is the size of B?

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Q: [-1 -1, |-5|,|5 4. 3 17

A: We have to find the dimNul(A), dim row A and rank. where A is the matrix consisting of columns…

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: Given a matrix A, shows that the dot product will not produce  the same result with the Hadamard…

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Q: If a matrix A has 2 linearly independent columns, then dimRow(A)=2. True O False

A: Please find the solution in the below step

Q: A 3x4 matrix A has Rank 1, then dim NUTLA %3D

A: The rank nullity theorem says that if T is a linear transformation form a vector Space V to vector…

Q: Given a matrix A = for what conditions on a, b, c, and d will the matrix not have an inverse?

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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: IF a 4*5 Matrix A has rank 2 , find dim(Null A), dim (Row A) and Rank A^T

A: Using Rank Nullity Thereom,

Q: a) If a n x (n + 5) matrix has rank n, find dim Nul A, dim row A and rank A".

A: Given n=2 Matrix A is 2×7 matrix  We need to find dim(Nul A) ,dim(row A) and rank AT

Q: If a 4x7 matrix A has rank 2, find nullity A, rank A, and rank A. nullity A =| rank A = rank AT

A: The given question has been solved in step 2.

Q: If a 4 by 4 matrix has det A = ½, find det(2A) and det(-A) and det(A2) and det(A-1 ).

A: Now,

Q: If AB is a 4 x 2 matrix and B is a 1 × 2 matrix, then the size of matrix A is

A: We can multiply two matrices only when the number of column in the first matrix must be equal to…

Q: Suppose that A is a 16 x 14 matrix that has 6 pivot columns. Then: (i) dim (ColA) is (ii) dim(ColA)-…

A:

Q: Given C and D are matrixes, and their products CD and DC exist, what can we tell about their…

A: Matrix multiplication is the process of multiplying two matrices using dot product. Dimension of a…

Q: Suppose A is a 3x3 matrix. Let B be the matrix obtained from A by performing the following…

A:

Q: f a n * ( n+5 ) matrix has rank n, find dim Nul A, dim row A and rank . where  n=9.

A: Given, A matrix of an order n×(n+5) has a rank n, where n=9. To find dim(Null A), dim(row A) and…

Q: For which value of k will the columns of the following matrix be linearly dependent?

A: objective is to find the value of k.

Q: If the __________ of a matrix is p× q, then p represents the number of __________ and q represents…

A: If the order of a matrix is p x q, then p represents the number of rows and q represents the number…

Q: If a 6 × 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT

A:

Q: If A is a 6×1 matrix and the sum A+B can be computed, what is the size of B?

A: Matrix addition. If A and B are matrices of the same size, then they can be added. (This is similar…

Q: If A is a 3x5 matrix, what is the largest possible value for its Rank? O 3

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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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Q: Find an elementary matrix E that corresponds to the row operation of subtracting – 6 times Row 1…

A: Applying elementary row operation on identity matrix I we get the elementary matrix E.Now we find a…

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.