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If A = [2 4,e= [-2:]: and '[E &]-3 compute each of the following: (e) (At)2At _ B2(D)AB3 202X X-13A2 _ 3A + 412(d)...

Question

If A = [2 4,e= [-2:]: and '[E &]-3 compute each of the following: (e) (At)2At _ B2(D)AB3 202X X-13A2 _ 3A + 412(d)

If A = [2 4,e= [-2:]: and '[E &]-3 compute each of the following: (e) (At)2 At _ B2 (D) AB3 202 X X -13 A2 _ 3A + 412 (d)



Answers

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

In this question, given that metrics A is equal to one, two for entry, and we are to compute we have to compute to A. Mm. This means that we are multiplying A by two, and we won't apply every entry In our metrics by two. So our resulting metrics will be Price moved to buy one, two by two, two by four and two x 3, and the answer here will be too well peach and six.

Here were given that metrics be is he go to minus three five, two in minus one. And it tricks eh is equal to one, two for entry. And we had to compute b minus A. And here we subtract the corresponding pairs. So Why. Not 3? He's going to subject one. We have five separating two we have to subjecting for And we have -1, separating three. And how resulting metrics here will be minus four, five minutes. Do we get Mhm. two minutes. We'll get managed to and -1 -3. We get minus four. And this is our final solution.

In this question we are given that metrics be Is equal to -3 five, two in minus one. In that metrics A. Is equal to one, two four and three. And we have to find B. A. He's actually the product of A. And B. Now to find the product 1st. Our metrics, how mattresses should be arranged at that. Uh The columns of the first matrix should be equal to the roles of the second metrics. So since we have equal columns on the first, equal to the rules on the second, matrix. Therefore we have we can have a product, we can multiply being A. And our resultant project Or our resulting metrics will be at two x 2. Matrix. So multiplying P. A row by column. So we have this role multiplying first caller to give us the first century. So we have minus three by one plus five x 4 is the first sentry. And ah first roll applying the second column to get the second entry. So we have minus three by two. Plus five by three is the second entry and we do likewise, two by one plus minus one by four. And lastly two by two plus minus one by three. And simplifying this. We have -3 plus 20 minus six plus 15, two minus four. And there we have four minus tweets and the resulting matrix will be 17. There were 15 -69. Yeah we have -2. There we have one and this is our final solution

In this question, we are given that the magics F is equal to 33 -1 -1 and the matrix A. Is equal to 12, four and three. And we had to compute three F plus to A. So Here we have three multiplying the metrics have plus two, multiplying the metrics A. And we might apply every entry. So we have nine, nine -3 and -3, heading with two full paint 10 6. And there's some here adding each corresponding entry nine plus to get 11 nine plus four. We get 13 minus three plus eight, we get five minus three plus six, We get positive three. And this is our final solution.


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