username3434964
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Could you help with the last question on my homework?

Attachment 761644

I’ve multiplied them together and that’s pretty much it so far. I’m not sure what to do next. I’m sure it’s either really obvious or I’ve made a mistake 😂

Attachment 761646
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ShantelleLuis
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I'm of no help my friend; 'attachments not found' :')
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username3434964
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(Original post by ShantelleLuis)
I'm of no help my friend; 'attachments not found' :')
Oh lol wait a minute I’ll try again
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username3434964
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(Original post by ShantelleLuis)
I'm of no help my friend; 'attachments not found' :'
 \begin{pmatrix} 2 & a \\ 1 & 3 \end{pmatrix} \begin{pmatrix}  a  \\ b \end{pmatrix} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}

I multiplied them together and got:

 \begin{pmatrix} 2a+ab \\ a-3b \end{pmatrix} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}

2a + ab = -1
 a - 3b = 2
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The Scotfather
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(Original post by Bill Nye)
 \begin{pmatrix} 2 & a \\ 1 & 3 \end{pmatrix} \begin{pmatrix}  a  \\ b \end{pmatrix} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}

I multiplied them together and got:

 \begin{pmatrix} 2a+ab \\ a-3b \end{pmatrix} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}

2a + ab = -1
 a - 3b = 2
Whats the question? Attachment still unavailable.
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username3434964
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(Original post by chrissy99)
Whats the question? Attachment still unavailable.
Oh lol the question is to find all possible pairs of values of a and b


 \begin{pmatrix} 2 & a \\ 1 & 3 \end{pmatrix} \begin{pmatrix} a \\ b \end{pmatrix} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}
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3pointonefour
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You have simultaneous equations so try rearranging the second equation in terms of a then substituting it into the top equation
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username3434964
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(Original post by 3pointonefour)
You have simultaneous equations so try rearranging the second equation in terms of a then substituting it into the top equation
Yeah I know its simultaneous equations, but I don't get what you're saying.

a = 2 + 3b ?
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DEͥSTͣIͫNY
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(Original post by Bill Nye)
 \begin{pmatrix} 2 & a \\ 1 & 3 \end{pmatrix} \begin{pmatrix}  a  \\ b \end{pmatrix} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}

I multiplied them together and got:

 \begin{pmatrix} 2a+ab \\ a-3b \end{pmatrix} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}

2a + ab = -1
 a - 3b = 2
Factorize and make "a" the subject of the first equation.
Then, substitute this into the second one, and solve for "b".
Or make "b" the subject in the second one, and substitute into first one.

There are other ways as well. It's basically a simultaneous equation
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The Scotfather
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(Original post by Bill Nye)
Yeah I know its simultaneous equations, but I don't get what you're saying.

a = 2 + 3b ?
Rearrange for A, sub A in to the top equation is what they are meaning I think. Do you know how to calculate the inverse of a matrix?
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(Original post by chrissy99)
Rearrange for A, sub A in to the top equation is what they are meaning I think. Do you know how to calculate the inverse of a matrix?
No xD. I've only had two lessons on them, and we have mainly been doing multiplying matrices and a few simultaneous equations with matrices
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Muttley79
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(Original post by Bill Nye)
 \begin{pmatrix} 2 & a \\ 1 & 3 \end{pmatrix} \begin{pmatrix}  a  \\ b \end{pmatrix} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}

I multiplied them together and got:
Where does the - 3b come from?
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username3434964
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(Original post by Muttley79)
Where does the - 3b come from?
Oh **** sorry, its meant to say -3 not 3 in the question
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Muttley79
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(Original post by Bill Nye)
Oh **** sorry, its meant to say -3 not 3 in the question
Ah, ha! Rearrange the second equation to make a the subject and then substitute into the first.
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The Scotfather
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(Original post by Bill Nye)
No xD. I've only had two lessons on them, and we have mainly been doing multiplying matrices and a few simultaneous equations with matrices
Then they'll want you to substitute in for a and rearrange
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(Original post by Muttley79)
Where does the - 3b come from?
(Original post by chrissy99)
Then they'll want you to substitute in for a and rearrange
(Original post by DEͥSTͣIͫNY)
Factorize and make "a" the subject of the first equation.
Then, substitute this into the second one, and solve for "b".
Or make "b" the subject in the second one, and substitute into first one.

There are other ways as well. It's basically a simultaneous equation
(Original post by 3pointonefour)
You have simultaneous equations so try rearranging the second equation in terms of a then substituting it into the top equation
Thanks everyone :P
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