I need help with this please (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?

a) A 7 by 9 matrix which has rank 5,The aim is to find the dimension of the four subspaces and what…

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

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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Similar questions

Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
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.)
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.
If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the column space of A?
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.
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.
What are the dimensions of the matrix below?
Good afternoon, Having some diffculty understanding subspaces. Should I create a matrix and find the nullspace?

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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?