HELP!! Is –41/2 equivalent to (–4)1/2? Why or why not?

1 answer:

8 0

No, they are not equivalent. The first term, -4 1/2 equals 4 whole units and one half unit. All negative. So it’s like you have someone 4 and 1/2 dollars.

The second term, (-4)1/2 means multiplying -4 times 1/2. Doing the multiplication for this gives you -4/2. Solving the division here is -2. It’s taking away 1/2 dollar 4 times.

I hope this helped. Happy to answer any questions you have.

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Treat the matrices on the right side of each equation like you would a constant.

Let 2X + Y = A and 3X - 4Y = B.

Then you can eliminate Y by taking the sum

4A + B = 4 (2X + Y) + (3X - 4Y) = 11X

==> X = (4A + B)/11

Similarly, you can eliminate X by using

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It follows that

$X=\dfrac4{11}\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\dfrac1{11}\begin{bmatrix}7&-10\\-7&11\end{bmatrix} \\\\ X=\dfrac1{11}\left(4\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\left(\begin{bmatrix}48&-12\\40&88\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\begin{bmatrix}55&-22\\33&99\end{bmatrix} \\\\ X=\begin{bmatrix}5&-2\\3&9\end{bmatrix}$