I thought i had to write \x^2 when typing an exponent guess i dont.
$\displaystyle \sum=mc^2$
$\displaystyle a^2+b^2=c^2$
$\displaystyle \frac{\pi^2-7}{3x+2}=28$
$\displaystyle \sqrt{5x^3-2x+4}$
$\displaystyle \left(\begin{array}{cccc}1&0&1&1\\0&1&1&1\\1&1&1&1 \\0&1&0&1\end{array}\right)$
there are many ways to do that. i always use the "array function" --if that's what it's called.
the code \left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right)
yields
$\displaystyle \left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right)$
also see post #5 here
$\displaystyle \frac{8x^2-3x+5}{7x+4}=4x^3$
This is awesome
$\displaystyle \sqrt[3]{27x^3}\Longrightarrow3x$
$\displaystyle (3x-8y)(2x^2-4xy+14y^2)\Longrightarrow$ Anyone know if I solved this correctly?
My answer is $\displaystyle 6x^3+4x^2y+74xy^2-112y^3$
Wow I'm bored
Heres another question:
$\displaystyle \left(\begin{array}{ccc}5&3&9\\3&0&7\\8&2&1\end{ar ray}\right)$ Solve the following matrix without a calculator
The steps i took to get my answer were as follows:
$\displaystyle 5\left(\begin{array}{cc}0&7\\2&1\end{array}\right)$
$\displaystyle -3\left(\begin{array}{cc}3&7\\8&1\end{array}\right)$
$\displaystyle 9\left(\begin{array}{cc}3&0\\8&2\end{array}\right)$
From there i got 5(-14)-3(-53)+9(6) Which led me to my answer of 143
Not positive if this is right. If it is not correct, can you post the steps you took to get the answer so I can see what I did wrong. Thanks.
you are correct, that is the determinant. you used the cofactor expansion method here, one of several methods to finding determinants of nxn matrices. there is another method you could have used to confirm your answer (it only works for 3x3 matrices) however, it's hard to describe the process in words, so just wait until your professor teaches you
Frankly I see no reason to learn any method for computing determinants other than the cofactor method. In order to do the 3 x 3 formula (the one where you put numbers beside the matrix and multiply down the columns) or any other you essentially have to learn a formula. And it doesn't generalize well to larger matrices. I prefer to learn the general method and leave it at that.
-Dan