MATRIKS

1. Jika matriks A diketahui seperti di bawah ini, maka determinan A adalah...

A. (a + b)(4a - b)
B. (4a + 4b)(a -b)
C. (4a + 2b)(4a + b)
D. (4a + 4b)(4a - 2b)
E. (4a + b)(4a - 4b)

Pembahasan :
det A = 4a² - 4b² = 4 (a² - b²)
det A = 4 {(a + b)(a - b)}
det A = (4a + 4b)(a - b)

2.Bila determinan matriks A adalah 4 kali determinan matriks B, maka nilai x adalah...

A. 4/3
B. 8/3
C. 10/4
D. 5/3
E. 16/7

Pembahasan :
det A = 4 det B
4^x (16^x) -  (-16) = 4 (108 - (-152))
4^x (4^2x ) + 16 = 4 (260)
4^3x = 4(260) - 16
4^3x = 4(260) - 4(4)
4^3x = 4 (260 - 4)
4^3x = 4 (256)
4^3x = 4. 4⁴
4^3x = 4⁵
3x = 5 
x = 5/3

3.Diketahui matriks A dan B seperti di bawah ini. Jika determinan matriks A = -8, maka determinan matriks B adalah...

A. 96
B. -96
C. -64
D. 48
E. -48

Pembahasan :
Determinan A 

det A = (aei + bfg + cdh) - (ceg + afh + bdi) = -8


Determinan B

 

det B = (-12aei + (-12bfg) + (-12cdh)) - (-12ceg + (-12afh) + (-12bdi))
det B = -12 { (aei + bfg + cdh) - (ceg + afh + bdi)}
det B = -12 det A
det B = -12 (-8)
det B = 96

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Milan Tomic

Hi. I’m Designer of Blog Magic. I’m CEO/Founder of ThemeXpose. I’m Creative Art Director, Web Designer, UI/UX Designer, Interaction Designer, Industrial Designer, Web Developer, Business Enthusiast, StartUp Enthusiast, Speaker, Writer and Photographer. Inspired to make things looks better.

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