# Matrix expansion

• August 7th 2012, 10:33 AM
Greymalkin
Matrix expansion
Not sure how to input matrices into latex but its an easy problem:

A=
|7 -4 -6 |
|2 0 -3 |
|1 2 -5 |

Evaluate |A| by expanding down the third column:
I get:
[-6(-1)4(3)]+[-3(-1)5(18)]+[-5(-1)6(8)]
=-6(3)+3(18)-5(8)
=-4

answer is supposed to be -10, which i've arrived at expanding another row and column, what am I doing wrong?(Clapping)
• August 7th 2012, 10:43 AM
Plato
Re: Matrix expansion
Quote:

Originally Posted by Greymalkin
Not sure how to input matrices into latex but its an easy problem:

A=
|7 -4 -6 |
|2 0 -3 |
|1 2 -5 | Evaluate |A| by expanding down the third column:

$-6(4)+3(18)-5(8)=-10$
• August 7th 2012, 10:48 AM
Greymalkin
Re: Matrix expansion
ahh silly mistake 1x0, thank you very much sir!
• August 7th 2012, 10:51 AM
HallsofIvy
Re: Matrix expansion
Quote:

Originally Posted by Greymalkin
Not sure how to input matrices into latex but its an easy problem:

A=
|7 -4 -6 |
|2 0 -3 |
|1 2 -5 |

Evaluate |A| by expanding down the third column:
I get:
[-6(-1)4(3)]

How did you get "3" here? $6\left|\begin{array}{cc}2 & 0 \\ 1 & 2\end{array}\right|= 6(4)$

Quote:

+[-3(-1)5(18)]+[-5(-1)6(8)]
=-6(3)+3(18)-5(8)
=-4

answer is supposed to be -10, which i've arrived at expanding another row and column, what am I doing wrong?(Clapping)
• August 7th 2012, 11:17 AM
Soroban
Re: Matrix expansion
Hello, Greymalkin!

Quote:

$A\:=\:\begin{vmatrix}7&\text{-}4&\text{-}6 \\2&0&\text{-}3 \\ 1&2&\text{-}5\end{vmatrix}$

$\text{Evaluate }|A|\text{ by expanding down the third column.}$

$\text{I get: }\:[\text{-}6(\text{-}1)^4(3)]+[\text{-}3(\text{-}1)^5(18)]+[\text{-}5(\text{-}1)^6(8)]$ . Not sure what all this is.
. . . $=\;\text{-}6(3)+3(18)-5(8) \;=\;-4$

Answer is supposed to be -10, which i've arrived at expanding another row and column.
What am I doing wrong?

Down the third column . . .

. . $\text{-}6\begin{vmatrix}2&0\\1&2\end{vmatrix} - (\text{-}3)\begin{vmatrix}7&\text{-}4 \\ 1&2 \end{vmatrix} - 5 \begin{vmatrix}7 & \text{-}4 \\ 2 & 0 \end{vmatrix}$

. . $=\;-6\underbrace{(4-0)}_{\text{Here!}} + 3(14 +4) - 5(0+8)$

. . $=\;-24 + 54 - 40$

. . $=\;-10$