can you please help regarding this matrix question

[Dennis]

I have been given the matrix question below, and matrix agebra is not my 'strong' area :-

Question:

. . . . .\(\displaystyle \left[ \begin{array}{rr}7&21\\21&68.25\end{array} \right]\,\left[ \begin{array}{r}x\\y\end{array}\right]\, =\, \left[ \begin{array}{r}15.75\\74.531\end{array}\right]\)

Answer: \(\displaystyle (x,\, y)\, =\, (-13.339,\, 5.1964)\)

Can you please help e and tell me if the answer i correct, and, (more important for me) , please sowme 'how' the answer solution i worked out (sep by step) . I appreciate your help. Thank you. Dennis

 

[stapel]

I have been given the matrix question below, and matrix agebra is not my 'strong' area :-

Question:

. . . . .\(\displaystyle \left[ \begin{array}{rr}7&21\\21&68.25\end{array} \right]\,\left[ \begin{array}{r}x\\y\end{array}\right]\, =\, \left[ \begin{array}{r}15.75\\74.531\end{array}\right]\)

Answer: \(\displaystyle (x,\, y)\, =\, (-13.339,\, 5.1964)\)

Can you please help e and tell me if the answer i correct

Are you saying that the "Answer" provided is yours, rather than the book's? If so, then plug it into the system of equations, and see if it works:

. . . . .7(-13.339) + 21(5.1964) = ??
. . . . .21(-13.339) + 68.25(5.1964) = ??

If you get "15.75" (approximately) for the first equation and "74.531" for the second, then your solution is correct. If not, then not.

...and, (more important for me) , please sowme 'how' the answer solution i worked out (sep by step)

You already have loads of step-by-step worked examples in your textbook, in your class notes, and in the various online resources you've reviewed in your studies. So one more worked example is unlikely to make any difference. To learn, one must do, so let's try that:

If your answer does not check, please reply showing your steps, and we'll be glad to help you find where things are going sideways.

Thank you!

 

[pka]

I have been given the matrix question below, and matrix agebra is not my 'strong' area :-

Question:

. . . . .\(\displaystyle \left[ \begin{array}{rr}7&21\\21&68.25\end{array} \right]\,\left[ \begin{array}{r}x\\y\end{array}\right]\, =\, \left[ \begin{array}{r}15.75\\74.531\end{array}\right]\)

Answer: \(\displaystyle (x,\, y)\, =\, (-13.339,\, 5.1964)\)

Can you please help e and tell me if the answer i correct, and, (more important for me) , please sowme 'how' the answer solution i worked out (sep by step) . I appreciate your help. Thank you. Dennis

Here is the correct solution

If you need steps, you can break it down bit by bit.

 

[Dennis]

Thanks Denis

Thanks Denis (with one 'n'). I often get spelt with one 'n' , so that's OK. I appreciate your help.

Hate to talk to someone with one more "n" than me...:cool:

You do realise that you have these 2 equations(?):
7x + 21y = 15.75 [1]
21x + 68.25y = 74.531 [2]

If you multiply [1] by -3, you get:
-21x - 63y = -47.25 [3]

Now add [2] and [3] together...get my drift?

 

[Dennis]

Thank you pka

Thank you pka. When Ilooked at the reply rm Denis, I got x = -13.3392 , y = 5.1964 . Thanks again.

Here is the correct solution

If you need steps, you can break it down bit by bit.

 

[Dennis]

Thank you stapel

Thank you stapel.

Are you saying that the "Answer" provided is yours, rather than the book's? If so, then plug it into the system of equations, and see if it works:

. . . . .7(-13.339) + 21(5.1964) = ??
. . . . .21(-13.339) + 68.25(5.1964) = ??

If you get "15.75" (approximately) for the first equation and "74.531" for the second, then your solution is correct. If not, then not.


You already have loads of step-by-step worked examples in your textbook, in your class notes, and in the various online resources you've reviewed in your studies. So one more worked example is unlikely to make any difference. To learn, one must do, so let's try that:

If your answer does not check, please reply showing your steps, and we'll be glad to help you find where things are going sideways.

Thank you!