find-k-if-the-deteminant-of-3-k-2-3-is-2-can-someone-please-teach-me-how-to-find-the-deteminant-of-a-3-3-matrix-

Question Number 33425 by Rio Mike last updated on 16/Apr/18

f i n d k i f t h e d e t e m i n a n t o f

(\begin{matrix} 3 k \\ 2 3 \end{matrix}) i s 2

c a n s o m e o n e p l e a s e t e a c h m e h o w

t o f i n d t h e d e t e m i n a n t o f a 3 \times 3

m a t r i x ?

Commented by Joel578 last updated on 16/Apr/18

9 - 2 k = 2

k = \frac{7}{2}

Commented by Joel578 last updated on 16/Apr/18

For 3 \times 3 matrice, you can learn from youtube or

textbooks

Commented by prof Abdo imad last updated on 17/Apr/18

i f A = (\begin{matrix} a b c \\ e f g \end{matrix})

(k l m

d e t A = a ∣_{l m}^{f g} ∣ - e ∣_{l m}^{b c} ∣ + k ∣_{f g}^{b c} ∣

= a (f m - l g) - e (b m - l c) + k (b g - f c) l e t t a k e

e x a m p l e

A = (\begin{matrix} 1 - 1 o \\ 2 1 3 \end{matrix})

(- 1 2 4)

d e t A = 1 ∣_{2 4}^{1 3} ∣ - 2 ∣_{2 4}^{- 1 0} ∣ + (- 1) ∣_{1 3}^{- 1 0} ∣

= 4 - 6 - 2 (- 4) - 1 (- 3)

= - 2 + 8 + 3 = 9 .

Answered by MJS last updated on 16/Apr/18

d e t (\begin{matrix} a & b \\ c & d \end{matrix}) = a d - b c

d e t (\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}) =_{- (a f h + b d i + c e g)}^{(a e i + b f g + c d h) -}

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