if-the-null-space-of-a-5-times-6-matrix-a-is-4-dimensional-what-is-the-dimension-of-the-row-space-of

Question

If the null space of a $5 	imes 6$ matrix $A$ is 4 -dimensional, what is the dimension of the row space of $A ?$

Runpeng Li · Accepted Answer

in this problem, we have Ah, matrix. That is five by six. Bye bye. 68 drinks. And we know that dimension off the nose. Face up. These matrix is five. Sorry for. And we need to figure out the dimension of the rose face A game. We apply the rank, the room first. So the rank off, eh? ISS and minus invention off. Announce yourself, eh? So that&#x27;s six minus four, which is, too, and that it is equal to do you mention up the rose face of a so

Subham Jyoti Mishra · Answer

the question. We have been given a methods here, which is by by six metrics. And we have been given that the diamonds, you know, space a quarter. For now, we have been asked to find off the diamonds and off problem space here. This is equal to rank. Okay. By rank Children, we have, uh and is it Jordan diamonds and all? Nothing. Hey, let&#x27;s rank up here. So therefore there any number off problems with his in the form of him? Cross him. So anything over six years 63 44 less the rain off here which employs the bank off here. It&#x27;s important to therefore the dimension off column space K is toe this two dimensional.

Runpeng Li · Answer

All right, so in this problem, you have matrix. That is seven by six. And we know no space estimation. That&#x27;s dimension, huh? Fire. So we need to find out the dimension of column space. Okay, so the dimension of the columns face, remember our note or in problem? Six. That is a dimension of the column space. Hey, it&#x27;s same as the rank obey. And at the same time, the rank by the lengthy REM rank up, eh? Is and minus dimension up the north face. Okay, so in this case, six dimension of space five. So the column space should have mentioned one.

Subham Jyoti Mishra · Answer

So we have a metrics there. It&#x27;s just 855 metrics. We have been given their Damien son off now space off air. They could have to, and we have to calculate in the dimension off road space off. So the time you know those space off here is equal. Do the diamonds, you know, column space off. If it&#x27;s just a word and minus, which is equally Adminis diamonds and no, no space off. This is coming from the ranked Europe, where Vang off plus diamonds and a lot of yeah, this in the form of payment to end so on his reported a five year You think this the demons, you know your space is getting by minus two, which is a tree.

Bobby Barnes · Answer

So in order for us to determine what this ball is possible dimension of Knoll a could be, um we can use the following so we can use the fact that we know the ring. So how do you still drink? Rank of a plus? The dimension of the knoll of a should be equal to S O over here. If this is m by in, it should be equal to end. So if we can figure out well, what should our maximum rank of the speech then we can use that to find our Matt or minimum dimension because Max Rank is saying the same thing as minimizing are no a dimension. Let&#x27;s go in and just draw six by four matrix. So 123456 Um, so six rows and then four columns everywhere with the red and green light intersect each other we have on entry. So the maximum rank we could have for this is going to be where we have four pivots here. So we have a pivot in each of the columns, so that implies that Max Ring is going to be or eso if we use that appear. So that&#x27;s gonna be four. Plus the dimension of Noel A is equal to well, in this case in its four. And well, if we subtract that over, that implies our minimum dimension of no a can be zero. So I should probably say men here. Yeah, so that is going to be the smallest possible that we can have.

Ankit Gupta · Answer

So in this question we have are two across three metrics being multiplied way at three cross for metrics. All right, so this three industry are same the then what is going to happen? These two terms are going to be removed, and the resultant metrics is going to be off the order to cross for so therefore also, this is a metrics, and this is being metrics small dimensions off. Every will be corrido to cross for So that&#x27;s my answer.

Problem

If $A$ is a $7 \times 5$ matrix, what is the larg…

Problem 12 Easy Difficulty

If the null space of a $5 \times 6$ matrix $A$ is 4 -dimensional, what is the dimension of the row space of $A ?$

Answer

dim row space of $A=\operatorname{rank} A=2$

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

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dim row space of $A=\operatorname{rank} A=2$

Linear Algebra and Its Applications

Anna Marie V.

Heather Z.

Kristen K.

Samuel H.

Vectors Intro

Vector Basics - Example 1

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Anna Marie V.

Heather Z.

Kristen K.

Samuel H.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications