how do you solve the simultaneous equations 2x + y = 9 and x - 2y = -8 using the matrix method?
$begingroup$
i first convert the bases into a 2x2 matrix and then i multiplied the inverse matrix by the 2x1 e/f matrix of 9 (on top) and -8 (on the bottom)
which gave me x = 5.4 and y = 5
however the answer sheets states that x= 2 and y=5
May i please have some help on where I'm going wrong? Am i not multiplying the signs correctly? thank you for your help.
matrices systems-of-equations matrix-equations
asked Apr 24 '16 at 17:02
m.am.a
21
$endgroup$
add a comment |
$begingroup$
i first convert the bases into a 2x2 matrix and then i multiplied the inverse matrix by the 2x1 e/f matrix of 9 (on top) and -8 (on the bottom)
which gave me x = 5.4 and y = 5
however the answer sheets states that x= 2 and y=5
May i please have some help on where I'm going wrong? Am i not multiplying the signs correctly? thank you for your help.
matrices systems-of-equations matrix-equations
asked Apr 24 '16 at 17:02
m.am.a
21
$endgroup$
$begingroup$
your approach is right , just look at the value of inverse , whether it is right , or whether you wrote the matrix wrong
$endgroup$
– avz2611
Apr 24 '16 at 17:04
add a comment |
$begingroup$
i first convert the bases into a 2x2 matrix and then i multiplied the inverse matrix by the 2x1 e/f matrix of 9 (on top) and -8 (on the bottom)
which gave me x = 5.4 and y = 5
however the answer sheets states that x= 2 and y=5
May i please have some help on where I'm going wrong? Am i not multiplying the signs correctly? thank you for your help.
matrices systems-of-equations matrix-equations
asked Apr 24 '16 at 17:02
m.am.a
21
$endgroup$
i first convert the bases into a 2x2 matrix and then i multiplied the inverse matrix by the 2x1 e/f matrix of 9 (on top) and -8 (on the bottom)
which gave me x = 5.4 and y = 5
however the answer sheets states that x= 2 and y=5
May i please have some help on where I'm going wrong? Am i not multiplying the signs correctly? thank you for your help.
matrices systems-of-equations matrix-equations
matrices systems-of-equations matrix-equations
asked Apr 24 '16 at 17:02
m.am.a
21
asked Apr 24 '16 at 17:02
m.am.a
21
asked Apr 24 '16 at 17:02
m.am.a
21
asked Apr 24 '16 at 17:02
m.am.a
21
asked Apr 24 '16 at 17:02
m.am.a
21
21
$begingroup$
your approach is right , just look at the value of inverse , whether it is right , or whether you wrote the matrix wrong
$endgroup$
– avz2611
Apr 24 '16 at 17:04
add a comment |
$begingroup$
your approach is right , just look at the value of inverse , whether it is right , or whether you wrote the matrix wrong
$endgroup$
– avz2611
Apr 24 '16 at 17:04
$begingroup$
your approach is right , just look at the value of inverse , whether it is right , or whether you wrote the matrix wrong
$endgroup$
– avz2611
Apr 24 '16 at 17:04
$begingroup$
your approach is right , just look at the value of inverse , whether it is right , or whether you wrote the matrix wrong
$endgroup$
– avz2611
Apr 24 '16 at 17:04
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint:
In matrix notation we have:
$$
Ax=b
$$
with
$$
A=begin{bmatrix}
2&1\1&-2
end{bmatrix}
qquad x=begin{bmatrix}
x\y
end{bmatrix}qquad
b=begin{bmatrix}
9\-8
end{bmatrix}
$$
so $$x=A^{-1}b$$
with
$$
A^{-1}=frac{1}{5}begin{bmatrix}
2&1\1&-2
end{bmatrix}
$$
answered Apr 24 '16 at 17:11
Emilio NovatiEmilio Novati
52.2k43474
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1756883%2fhow-do-you-solve-the-simultaneous-equations-2x-y-9-and-x-2y-8-using-the%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint:
In matrix notation we have:
$$
Ax=b
$$
with
$$
A=begin{bmatrix}
2&1\1&-2
end{bmatrix}
qquad x=begin{bmatrix}
x\y
end{bmatrix}qquad
b=begin{bmatrix}
9\-8
end{bmatrix}
$$
so $$x=A^{-1}b$$
with
$$
A^{-1}=frac{1}{5}begin{bmatrix}
2&1\1&-2
end{bmatrix}
$$
answered Apr 24 '16 at 17:11
Emilio NovatiEmilio Novati
52.2k43474
$endgroup$
add a comment |
$begingroup$
Hint:
In matrix notation we have:
$$
Ax=b
$$
with
$$
A=begin{bmatrix}
2&1\1&-2
end{bmatrix}
qquad x=begin{bmatrix}
x\y
end{bmatrix}qquad
b=begin{bmatrix}
9\-8
end{bmatrix}
$$
so $$x=A^{-1}b$$
with
$$
A^{-1}=frac{1}{5}begin{bmatrix}
2&1\1&-2
end{bmatrix}
$$
answered Apr 24 '16 at 17:11
Emilio NovatiEmilio Novati
52.2k43474
$endgroup$
add a comment |
$begingroup$
Hint:
In matrix notation we have:
$$
Ax=b
$$
with
$$
A=begin{bmatrix}
2&1\1&-2
end{bmatrix}
qquad x=begin{bmatrix}
x\y
end{bmatrix}qquad
b=begin{bmatrix}
9\-8
end{bmatrix}
$$
so $$x=A^{-1}b$$
with
$$
A^{-1}=frac{1}{5}begin{bmatrix}
2&1\1&-2
end{bmatrix}
$$
answered Apr 24 '16 at 17:11
Emilio NovatiEmilio Novati
52.2k43474
$endgroup$
Hint:
In matrix notation we have:
$$
Ax=b
$$
with
$$
A=begin{bmatrix}
2&1\1&-2
end{bmatrix}
qquad x=begin{bmatrix}
x\y
end{bmatrix}qquad
b=begin{bmatrix}
9\-8
end{bmatrix}
$$
so $$x=A^{-1}b$$
with
$$
A^{-1}=frac{1}{5}begin{bmatrix}
2&1\1&-2
end{bmatrix}
$$
answered Apr 24 '16 at 17:11
Emilio NovatiEmilio Novati
52.2k43474
answered Apr 24 '16 at 17:11
Emilio NovatiEmilio Novati
52.2k43474
answered Apr 24 '16 at 17:11
Emilio NovatiEmilio Novati
52.2k43474
answered Apr 24 '16 at 17:11
Emilio NovatiEmilio Novati
52.2k43474
52.2k43474
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1756883%2fhow-do-you-solve-the-simultaneous-equations-2x-y-9-and-x-2y-8-using-the%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
your approach is right , just look at the value of inverse , whether it is right , or whether you wrote the matrix wrong
$endgroup$
– avz2611
Apr 24 '16 at 17:04