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Let A =a2Assuming has a value for which A-1 exists (see previous question) find A-12(a? 1)1 _ a2not enough info to answer the question2(1 a2...

Question

Let A =a2Assuming has a value for which A-1 exists (see previous question) find A-12(a? 1)1 _ a2not enough info to answer the question2(1 a2

Let A = a2 Assuming has a value for which A-1 exists (see previous question) find A-1 2(a? 1) 1 _ a2 not enough info to answer the question 2(1 a2



Answers

Let $$\mathbf{A} :=\left[ \begin{array}{ll}{2} & {4} \\ {1} & {1}\end{array}\right] \quad$$ and $$\quad \mathbf{B} :=\left[ \begin{array}{rr}{-1} & {3} \\ {5} & {2}\end{array}\right].$$
Find: $$ (a) \mathbf{A}+\mathbf{B} . \quad $$ $$ (b) 7 \mathbf{A}-4 \mathbf{B} $$

Okay. We weren't in seven or eight times be its unique modification. We do the rose off the Matrix. Private colleges, the 2nd 1 So, for instance, if I went to find, you know what I said was fine. Second row here. First column we go. Second row, First column one times three is 33 times minus minus three. So it's gonna be zero. Now, let's take the second row. Second column one times minus takes. Queen minus two times. One times 333 months, two is one. Okay, Now we want the top, right? I'm going to stop in a second. Comment. Like mixing this up instead of, you know, 1112211212 tickets. So you go 12 here. So but 1 to 2 times zero on here. Got 123 months. 11 time stories three and then modesty to be a whoops. We're actually identity here. Nice

Before we talk about how to multiply matrices, let's review how we determine if the multiplication is even defined. Multiplication is defined when the number of columns in the First Matrix is equal to the number of rows in the second Matrix. In this example, Matrix A is a two by two Matrix and Matrix B is a two by three. So we noticed that the First Matrix has two columns and the Second Matrix has two rows. So therefore the multiplication is defined and the resulting matrix will be a two by three matrix. So let's set that up. The Matrix A B is going to be two rows by three columns. Okay, so let's figure out what goes into those spaces here. We are going to look at the row of the first Matrix and the column of the Second Matrix, and what we're going to do is multiply these two elements and add that to the product of these two elements. So, for example, one times two is two plus three times three is nine, and we're going to do the same thing for these other elements. So here notice that this is the first row second column. So we're going to look at this first row and the second column. So one times zero is zero. Yeah, plus three times negative. Two is negative. Six. Looking at this space here, which is the first row. Third column, first row, third column. So one times negative. Four. It's negative. Four plus three times six, which is 18. And we're going to do the same thing here. So this element here this spot is the second row first column. So we're gonna be looking at the second row. First column two times two is four plus negative one times three is negative. Three second row second column, two times zero Hey, zero plus negative. One times negative two is to. And then in this last one, which is the second row third column So we would be doing negative two. I'm sorry. Positive. Two times Negative four, Which is negative. Eight plus negative. One times a positive six, which is negative. Six. And so now our matrix is just those sums, so a B is going to be two plus nine is 11 0 plus negative. Six is negative. Six. Negative four plus 18 is 14 4 plus negative. 30 years. 10 plus two is two negative eight plus negative. Six is negative 14, and that is that product. Now. If I wanted to multiply the Matrix B times a just flipping those around. Well, before I do that, I better double check to make sure that the multiplication is even defined. So remember, Matrix B is a two by three matrix and A is a two by two and you'll notice that The Matrix has three columns and the A tricks has two rows. And since those don't match, that means that this multiplication is not defined so we cannot multiply these two together.

For the full problem. A legal now calculates is a magics a plastic magic speak. So Mac chicks a Choose the r 05 Chu er because one knocked everyone too. They are old three negative Chu So we pass the same element, you know, sing place together. So it's true past Want zero negative one Fires cost two and two class hero One past history were in past Next time too. So the acid will be three negative 17 negative one for two. So this is the answer for the Mac tricks. A pross metrics be for the problem to re calculate seven A. My nurse for B rage means seven times two old five to Woz minors. Four tons, one, my ass. Want to funeral three? No, to chew. So for the for the first part, we just Tom seven for each element. So the first part's wealthy 14 p r o 35 40 shover several then therefore those ah, third part would do the same thing we come every element in the magics be to a time for so it will be four. Nothing. 480 12. No, you're right. Then we go on out calculator the thieves Part of these parts together, this is theme as paws were just too minors. Every element in the same place together. So is 14 Mylar for the R O Minor's name came for so Tiffany miners eight 14 by their fear 07 miners, 12 federal miners Nectar rate cool. So after will be 10 4 turned tests Our 14 year parents five. Bender 15.

Just push Every will ask to multiply two matrices. They're a equals two one to hear negative through. We buy in two by two and he is this so retold. Don't want to do a times B A B so a got B you close to He's gonna I'm just ready at one big toe to So it's horizontal. A times already ropey because eggs first time be second. So I want to thank you Want. It's negative for two times. Two is four. Now let's move here. Once a theory is a theory and tutors for is an eight. Next, we have the second row here negative three times and get it want. That's a three and five times two. That's a 10. That's like a road time second column. Good negative. Three times the re negative nine five times for last 20. So that's our answer. Now it's just simplify. Do arithmetic negative for any kind of negative one plus for three three plus 8 11 three plus 10 13 and a less is 11


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