If A is 5x4 matrix, and rank(A) = 1, then its nullity is 3.

Q: If A is an 7 x 12 matrix, then what is rank A² + dim nul (A²) equal to? Your

A: We can solve this as follows:

Q: If a matrix A is 3 x 7, and we know nothing else about it, explain why its columns must be linearly…

A: Given Ais a 3×7 matrix then we have to explain why its columns are linearly dependent.

Q: Find an SVD of the matrix. -6 5 A = 0 6

A: We have to general eigenvalue and eigenvectors to find Singular Value Decomposition of matrix A We…

Q: 6. Find the inverse of the matrix if it exists by using elementary row operation, 2 4 1 -1 1 -1

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Q: If X is an unknown matrix And A and B are known : [A]×[x]=[B]_ 5x5 5×1 [x] = ?

A: Given matrix A is of order 5×5 and matrix B of order 5×1 and A5×5×x=B5×1 We have to find the matrix…

Q: If A is an 3× 4 matrix and the nullity of A equals 2, find the rank of A .

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Q: Explain why the matrix A + C does not exist.

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Q: If A = (aij) is the matrix of the quadratic form 7x + 5x, + 2x – 6x1x2 + 12x1x3 – 10x2x3, then the…

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Q: Suppose A is 17x17 matrix with A^29=0 Then A^17=0.

A: Here given that A is 17×17 matrix and A29=0.

Q: If matrix A is 12 xc and matrix K is 4 x t, their product AK is r x 7, what are the values of c, t,…

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Q: What is a, if A = 2 4 is a singular matrix ? a Simplify (1+x)(1+x²)(1 – x + x?) in descending order…

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

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Q: 1 What value of x satisfies the matrix equation -2

A: Number of Multiple questions as per our company guidelines we are supposed to answer only first…

Q: Suppose that  |A| + |B| = |A + B| , find a 2x2 matrix for A and B

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Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

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Q: What does it mean to say that A is a matrix with dimension m x n?

A: Our Aim is to tell that what is meant by a matrix A which is havingdimension m×n.

Q: If A = [1 2 3], which type of the given matrix A ?

A: Given Matrix A=[1  2  3 ]1×3  Here number of row=1  Number of columns=3

Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

A: Given: Where, X is a diagonal matrix of A, then 7X is also diagonalizing matrix of A. To determine:…

Q: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

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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: 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: Suppose that A is a 9 x 5 matrix, and that B is an equivalent matrix in echelon form. If the number…

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Q: determine the general solution to the system x′= Ax for the given matrix A.

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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: If matrix A is of order 3x1 and matrix B is of order 4x3, then the order of matrix BA is 4x1 O 1x4…

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Q: Suppose that A is an 11 x 4 matrix, and that B is the rref of A. If the number of leading columns of…

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Q: If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

A: Consider the provided matrix, Given, A is a 6 x 8 matrix. Since, the rank of A equals the number of…

Q: If A is an invertible square matrix that is row equivalent to matrix B , then both A and B are row…

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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 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: For skew anti-symmetric matrix, the sum of its entries is (A 1 В -5 10 E -1

A: We want to find sum of entries of skew anti-symmetric matrix.

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: If A = 1 y and the transpose of the matrix is equal to the inverse of the matrix then y =

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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: Find the augmented matrices of th e linear systems x - y = 0 ,2x+y=3

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Q: Given 4x6 matrix A with rank(A) s3, the nullity n of A must be

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Q: If A is m x n matrix and Ax b has no %3D solution for some b. then

A: The rank r of a matrix is the number of column (row) pivots, it must be less than equal to m and n.…

Q: If a 5x8 matrix A has rank 3, find nullity A, rank A, and rank A'. nullity A = rank A = rank A' =

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Q: If the first two rows of a matrix A are equal and the matrix product AB is defined, then the first…

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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: Give the rank and the nullity of the matrix. 20 -2 A = rank(A) = nullity(A) =

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Q: Could a 4 x 7 matrix have dim Col A​=5 and dim Nul A​ = 2?  Justify your answer

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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: Give an example of a 4 by 4 matrix A, which is not symmetric, however A is symmetric.

A: A square matrix is said to be symmetric if it is symmetric about the main diagonal.

Q: If A is an n × n matrix, what are the entries on the main diagonal of A − AT ? Justify your answer.

A: Given A is an n x n matrix, we need to find the entries on the main diagonal of A- AT. Consider a 2…

Q: Let A be a 3x3 matrix, and let u₁ and u₂ be the first two columns of A. Assume that u₁ and u₂ are…

A: Here, u1 and u2 are the first two columns of the matrix A and they are not parallel.  That implies…

Q: Find the 2 x 2 matrix A, if 2 (A" – 212x2)-

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Q: Find c such that the number of the pivots to the matrix below is 2: 1 1 1 -1

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Q: The maximum number of linearly independent 7x2 matrices is 07 6. O 2 O 1 O 14

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