Answered: (a) If a 7 by 9 matrix has rank 5, what… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

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(a) If a 7 by 9 matrix has rank 5, what are the dimensions of the four subspaces?
What is the sum of all four dimensions?
(b) If a 3 by 4 matrix has rank 3, what are its column space and left nullspace?

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Solve: (a) If a 7 x 9 matrix A has rank 5, what are the dimensions of the fourfundamental subspaces of A? (b) If a 3 x 4 matrix A has rank 3, what are the dimensions of R(A) and N(AT)?
2. For each matrix A of Problem 1, write down orthonormal base for all four fundamental subspaces.(This can be read off from your answers to Problem 1.)
What can be said about Nul A if A is a 5×7 matrix? Could it be the zero subspace? Why or why not?
Suppose A is 10 by 10 and A2 = 0 (zero matrix). So A multiplies each column of A to give the zero vector. This means that the column space of A is contained in the __ . If A has rank r, those subspaces have dimension r � 10 � r. So the rank is '(' � 5.
Good afternoon, Having some diffculty understanding subspaces. Should I create a matrix and find the nullspace?
Find a basis for the space of all 2 by 3 matrices whose columns add to zero. Find a basis for the subspace whose rows also add to zero.
Make 2 multipart questions with 3 parts using the any of the following topics of "Matrix Operations, Subspaces, Subspaces Assosiated with Matricies, Basis, Dimension and rank, Introduction to Linear Transformation, Markov Chains, Complex Numbers". Make sure to explain in each part how the question would be benefical to a student answering the question.
Questions about Singular Valued Composition (SVD) and vector subspace. If the value of the determinant is 0, the inverse matrix cannot be obtained, so a similar inverse matrix is obtained using SVD and specific value decomposition. So we got eigenvalues and eigenvectors in this way. But I wonder why this result comes out when one of the two eigenvectors is the year of homogenous equation and the other is the base of the row space. The subject is linear algebra.
Is W=set of upper triangular 3x3 matrices a subspace of V= all 3x3 matrices? Support your answer to show why or why not.
What is a matlab (matrix laboratory)?
A matrix whose row are the rows of the unit matrix but not necessarily in natural order is called * Unit Matrix Scalar Matrix Permutation Matrix Null Matrix
How do the dimensions of the null space and column space of a matrix relate to the number of lead and free variables in the reduced row echelon form of the matrix? Explain.

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