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Math Help - Matrice - Ax=b A^-1b =x

  1. #1
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    Matrice - Ax=b A^-1b =x

    Hi

    I am hoping I am in the right spot - it is a linear algebra class but 1st year so take pity on me.....

    A is 1 1 1 1
    2 3 4 4
    3 4 4 4
    4 5 4 5

    B is 4
    5
    6
    3

    So let's pretend that I did the calculation of A^-1 correctly....

    I got

    1 0 0 0 -1 0 -2 2
    0 1 0 0 -4 3 -2 8
    0 0 1 0 1 0 1 -1
    0 0 0 1 0 -1 0 5

    Now how do I tie A^-1 back to B do I really just multiply them and how does this tell me what is x1 and x2 etc.

    Thanks for any insight you can give me....
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  2. #2
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    Quote Originally Posted by calcbeg View Post
    Hi

    I am hoping I am in the right spot - it is a linear algebra class but 1st year so take pity on me.....

    A is 1 1 1 1
    2 3 4 4
    3 4 4 4
    4 5 4 5

    B is 4
    5
    6
    3

    So let's pretend that I did the calculation of A^-1 correctly....

    I got

    1 0 0 0 -1 0 -2 2
    0 1 0 0 -4 3 -2 8
    0 0 1 0 1 0 1 -1
    0 0 0 1 0 -1 0 5

    Now how do I tie A^-1 back to B do I really just multiply them and how does this tell me what is x1 and x2 etc.

    Thanks for any insight you can give me....

    So apparently you have Ax=b ,and in full form, according to what you wrote, \begin{pmatrix}1&1&1&1\\2&3&4&4\\3&4&4&4\\4&5&4&5\  end{pmatrix}\,\begin{pmatrix}x_1\\x_2\\x_3\\x_4\en  d{pmatrix}=\begin{pmatrix}4\\5\\6\\3\end{pmatrix}

    Now, assuming A is invertible, we get Ax=b\Longleftrightarrow x=A^{-1}b , so assuming you did calculate the inverse of A correctly , you

    get \begin{pmatrix}-1&0&-2&2\\-4&3&-2&8\\\;\;\;1&0&\;\;1&\!\!\!-1\\\;\;\;0&\!\!\!-1&\;\;0&5\end{pmatrix}\begin{pmatrix}4\\5\\6\\6\en  d{pmatrix}=\begin{pmatrix}x_1\\x_2\\x_3\\x_4\end{p  matrix} , and the you only do the matrix product on the left to find out what the vector x (i.e., x_1,x_2,...) is.

    Unfortunately, your calculation of A^{-1} is incorrect, as multiplying it by A we do NOT get 0 in the entry 1-2, as we should...so check this and then do as above.

    Tonio
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