determine-the-dimensions-of-nul-a-and-mathrmcol-a-for-the-matrices-shown-in-exercises-13-18-aleftb-2

Question

Determine the dimensions of Nul $A$ and $\mathrm{Col} A$ for the matrices shown in Exercises $13-18$ .
$$
A=\left[\begin{array}{rrrrrr}{1} & {3} & {-4} & {2} & {-1} & {6} \ {0} & {0} & {1} & {-3} & {7} & {0} \ {0} & {0} & {0} & {1} & {4} & {-3} \ {0} & {0} & {0} & {0} & {0} & {0}\end{array}ight]
$$

Runpeng Li · Accepted Answer

So in this problem, we first need to find find Ah, number three variables forgiven me tricks. And then we need to find the number of people columns up there. Keep meeting. So, um, seems to give them a trick. Please is already, uh, it&#x27;s already ain&#x27;t the real reduced form. So we can Well, I will persist right down the matrix. Just just for information. This will be, um 13 inactive for two, 21 81 sticks and 00 one 93 70 And there was Hero one. Sir, we have three zeros for this. What? They call him up with 1/3 row. That is 000 14 Letter three and the last rule his whole zeros. Okay, so for this giving matrix, we can find that the people call him ISS. The first column They&#x27;re calling and forth color. So that would be Call him a his three. Okay, so what about the number three variables here? So check the three variables we have. First, there are six variables here. We first have X five plus four us for X six plus. Sorry, Linus. Three x so well, Yeah, We start with the export. Sorry should be explore plus or x five minus three x six, which is cereal. Okay, so from the second rule, we have x three minus three. Explore us seven. It&#x27;s five is zero and from the first rule, we have x one plus three extra checks, too. Minus four x three us two x four minus minus one. Thanks, fi plus six x six. Okay, we&#x27;ll do this step a step. So from this first question we have explore will be determined by x five and experience. So So we know, we know first X five and x x six are free variables. So what&#x27;s more, we have x three be determined by explore next fight, but export can be determined by X files. Maggot never have six. So at three can be determined by the pre variable X five with six. So So we&#x27;re done for the second question and for the first equation, we have x three X for X 56 are all it will be done and next to cannot be done by x five and excess exit. So we have to set It&#x27;s too as a three variables. So this is our set off three variables. So what? That means no off, eh? ISS three

Runpeng Li · Answer

problems. We&#x27;re keeping a three by three matrix. So that is one or collective 107 zero. Okay, so, um, we can first observe how many people call him. So we&#x27;re there. Be So there are one and two conway on Colin to so that that is too so about free variables. We first have seven of x two Cyril and x one plus four x two minus x three. It&#x27;s cereal, so that gives X one can be determined by X three. So that is X one equals x three and x two is always do so free. Better balls. We have only one, so no a it&#x27;s one.

Runpeng Li · Answer

a queue of matrix is two by two matrix, which is three four connective, 6 10 Okay, so, in order to determine the dimensions, um, first transformed this matrix thio reduced ashen of form. So this will be three. I&#x27;m sorry. Three or and we use second role. Plus, why sell the first room? So that would be zero. I saw a bit of personal eight. 18. So that gives X two. It&#x27;s cereal and X one could be ex want us or ex too, is you? So that means everything is cereal. Because we have X to zero and plugging into this equation, we have x one will be zero to so no A it is zero. What about a column? Obey. This dimension will turn out to be, uh, too, because we have two columns, have two columns with the people positions. So we have two people columns so that that is too

Thomas Emment · Answer

case. We want to determine the dimensions off this matrix on dimensions. Matrix are It&#x27;s rose on dhe, its columns. So first off was done with the rose. How many we got? 123 So three rows on. Now he&#x27;s finally columns we&#x27;ve got Well, I&#x27;ve got 12344 columns. So this is gonna be a three by four matrix.

Nyah Kshatriya · Answer

for this problem. We have two Major sees A and I, which is the identity matrix. And we want to show that a multiplied by a multiplied by I is equal to a and that I multiplied by a is equal to a as well. And so because it&#x27;s a four by four matrix I you and put it the Matrix into a matrix calculator. And I am put it the identity matrix as B. And so when we might play a times B, you can see that we get the same four by four matrix that is equal to a. And then you can also see that when we want to play B times A, we get the same matrix a again. So the shows that any matrix multiplied by the identity matrix will result in that same original matrix.

Mark Augustyn · Answer

we&#x27;re gonna take The Matrix. Negative. Three negative for eight and 10 and we&#x27;re going to multiply by the identity matrix 1001 Okay, for my matrix multiplication. Remember, we multiply across and then down. So negative three times one plus eight time zero and then on the bottom row, we have negative four times, one plus 10 times zero, and then we&#x27;re going to the same thing. But with the second column, So negative. Three times zero, They&#x27;re negative. Three times zero plus eight times one and then negative. Four times zero plus 10 times one. Okay, They were gonna simplify this in the first spot. Their negative three times one is negative, three plus zero. So this would be negative. Three. And the bottom spot here, negative four times one time or plus 10 times zero would just be the negative four in the top spot. Negative. Three times there are zero plus eight times. One which is just eight, and then negative. Four times 00 plus 10 which would be 10. So this was matrix eight times the identity matrix. Now I need to do the other order. I need to take the identity times the original. Okay, so the identity matrix is 1001 and then a matrix A is negative. Three negative 48 intent. Okay, so following its similar set of steps, we&#x27;re going to multiply across and down, so we&#x27;ll have one times negative. Three plus zero times negative. Four zero times negative, three plus one times negative. Four one times eight plus zero times 10 and then zero times eight plus one times 10. Okay, so then we just need to simplify this. So one times negative three is negative. Three plus zero. So that first spot there&#x27;s negative. Three. Let&#x27;s go down zero times negative. Three plus negative. Four would be negative for one times eight plus zero is eight, and then zero plus 10 is 10. Okay, So what we&#x27;ve shown here is that a times I your identity matrix is equal to your identity Times matrix A in which is just equal to matrix a

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Determine the dimensions of Nul $A$ and $\mathrm{…

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