5

0 K 4 I3 2 1 1 I [ 9 7 E I 5 % 3 > 1 } F 8 8 3 8 + 1 8 | J 1 8283 [ 1 3826 We L E L 1 r8:2 1 1 E 9 1} 1 4 ; V 4 0 < 0 4 | 4 0...

Question

0 K 4 I3 2 1 1 I [ 9 7 E I 5 % 3 > 1 } F 8 8 3 8 + 1 8 | J 1 8283 [ 1 3826 We L E L 1 r8:2 1 1 E 9 1} 1 4 ; V 4 0 < 0 4 | 4 0

0 K 4 I3 2 1 1 I [ 9 7 E I 5 % 3 > 1 } F 8 8 3 8 + 1 8 | J 1 8283 [ 1 3826 We L E L 1 r8:2 1 1 E 9 1 } 1 4 ; V 4 0 < 0 4 | 4 0



Answers

\begin{aligned}
&A=\left[\begin{array}{ll}
1 & 2 \\
4 & 3
\end{array}\right], \quad B=\left[\begin{array}{rr}
-3 & 5 \\
2 & -1
\end{array}\right]\\
&\mathbf{C}=\left[\begin{array}{rr}
1 & -1 \\
-1 & 1
\end{array}\right], \quad \mathbf{D}=\left[\begin{array}{ll}
1 & 1 \\
1 & 1
\end{array}\right]\\
&\mathbf{E}=\left[\begin{array}{ll}
1 & 3 \\
2 & 6
\end{array}\right], \quad \mathbf{F}=\left[\begin{array}{rr}
3 & 3 \\
-1 & -1
\end{array}\right]\\
&0=\left[\begin{array}{ll}
0 & 0 \\
0 & 0
\end{array}\right], \quad \quad \mathbf{I}=\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]
\end{aligned}
$$\mathbf{E}+\mathbf{0}$$

And one more matrix modification here. This time of the times a Roman. eight times I Okay. We will run through what how this works. Okay, a resultant two by two. Matrix again, we're just following our matrix multiplication rules. Row one, column one. One times one. The Stereo Times four will give us a one. Okay, top right. That row one, column two, one times two, zero times three. That will give us a two there. Mhm. Caught him. Right. Row two column oil one time zero. That's four times 1 for their and then I lost out on the bottom right, We know his road to call him too. Zero times two. It was one times 3 for three. His matrix looks familiar. Again, it is a matrix. So multiplying the identity on either side here, either on the left or on the right will not change the matrix that that identity is multiplied.

They were multiplying matrices, E and F. Together here. Eight times F. We know this will give us a two by two matrix as a result. So. Top right element row one, column 11 times three plus three times negative one. Get zero there. Okay. Top right. Row one column to one times three was three times negative one. This is another zero there. Okay. Moving our way through. It just takes a bit of practice. These guys working through all the elements, say it to yourself in your head or out loud. If you want. Row one column, try road to column one. Two times three plus six times negative one. Okay, It's gonna give us another zero there. I guess. I think we're getting zero matrix out here, but we'll check with the last element Road to college too. Two times 36 times negative one. Another zero out there. Okay, so our result here is again zero metrics.

Matrix modification here. This time we got the zero matrix times F. Okay, If you don't already know the zero matrix times anything, we'll leave the zero and all of our spots. We'll just see why hand. Okay, so let's go through and do matrix modification. Row one, column one, zero times three. Zero times negative one. We know that's going to be zero. Okay, next spot in top right. Row one. Column one. Well, that's the same calculation. We just did we know that's going to give us zero. Okay, we can avoid a little bit of work there. Bottom left road to column one. Again, the same calculation we've already done because of how the numbers are falling here. The multiplying by zero in each spot is given a zero everywhere as well. Okay, last time, row two, column to again, pretty easy to see. That's gonna give us there. Okay? It's the same with real numbers at multiplying zero by anything, we'll give you zero. Just in this case it gives us the zero metrics rather than the real number zero.

You've got it all set up here. Okay. Following our order of operations, we know we have to do the multiplication first. So this three and those two are going into their respective matrices first. Before we try and add Okay, hopefully we're getting good at matrix modification by now, so we could jump straight to here. We've also done these to individual pieces already in previous questions. Now we just add these two matrices together. So this nine plus is two for 11. This nine puts this 4, 13. This negative three plus. This eight for five. This negative three plus. This six for three. Okay, so just following the same order of operations, we would with a regular real numbers were doing the same with matrices violence or 11 13 53


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