determinants !

**arsenal12345** · August 4th 2012, 06:44 PM

Find the determinants of the following matrices

a) u= 1 2 answear i got is -13
3 4
w= 6 7 answear i got is -1
7 8

a = 0 3 -1 answear i got is 1
0 2 -1
1 1 1

B = 0 1 2 answear i got is -6
1 0 2
2 2 2

In Mr Jones high school class there are 32 students. There are 20 students who
take mathematics, 15 students who take Physics, and 10 students who take
both. How many students don’t study either of these two subjects. Use the
notation of set theory to describe this situation

In each case compute f g(x) where
f(x) = 2x + 3 and g(x) = x2 − 1.
f(x) = x2 − 1 and g(x) = 2x + 3.

can some 1 help me solve these ?? i did the ones i could please cheack my answear and help me solve the ones i could not do , k thnks cheers !!

**GJA** · August 4th 2012, 08:11 PM

I would check the determinant on your first matrix again. I got something different. Let me know what you get the second time around to see if we're in agreement.

**arsenal12345** · August 4th 2012, 08:56 PM

i redid it i got -11 is that what u got ?? can u solve the 3 problems below that ?/ i am stuck on them too!

**Soroban** · August 4th 2012, 09:01 PM

Hello, arsenal12345!

Find the determinants of the following matrices.

$u\:=\:\begin{pmatrix}1&2 \\ 3&4\end{pmatrix}$ . Answer i got is -13. / How?

$\begin{vmatrix}1&2\\3&4\end{vmatrix} \:=\:(1)(4) - (2)(3) \:=\:4-6 \:=\:-2$

$w \:=\:\begin{pmatrix}6&7\\ 7&8 \end{pmatrix}$ . Answer i got is -1.

This is the only one that is correct.

$a \:=\:\begin{pmatrix}0&3&\text{-}1 \\ 0&2&\text{-}1 \\ 1&1&1\end{pmatrix}$ . Answer i got is 1.

$\begin{vmatrix}0&3&\text{-}1 \\ 0&2&\text{-}1 \\ 1&1&1 \end{vmatrix} \;=\;0\begin{vmatrix}2&\text{-}1 \\ 1&1 \end{vmatrix} - 3\begin{vmatrix}0&\text{-}1\\1&1\end{vmatrix} - 1\begin{vmatrix}0&2\\1&1\end{vmatrix}$

. . . . . . . $=\;0(2+1) - 3(0+1) - 1(0-2) \;=\;0-3+2 \;=\;-1$

$B \:=\:\begin{pmatrix} 0&1&2 \\ 1&0&2 \\ 2&2&2\end{pmatrix}$ . Answer i got is -6.

$\begin{vmatrix}0&1&2 \\ 1&0&2 \\ 2&2&2\end{vmatrix} \;=\;0\begin{vmatrix}0&2\\2&2\end{vmatrix} - 1\begin{vmatrix}1&2\\2&2\end{vmatrix} + 2\begin{vmatrix}1&0\\2&2\end{vmatrix}$

. . . . . . . $=\;0(0-4) - 1(2-4) + 2(2-0) \;=\;0 + 2 + 4 \;=\;6$

**arsenal12345** · August 4th 2012, 10:31 PM

haha thnx , looks like i counted wrong !

any luck with the rest ?

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