Editorial - Matwa - Soal TKA 2

Problem 1

Find the mean.

mu equals the fraction with numerator 8 plus 9 plus 10 plus 11 plus 12 plus 12 plus 12 plus 14 and denominator 8 equals 11

sigma squared equals the fraction with numerator the sum of open paren x minus mu close paren squared and denominator n equals the fraction with numerator 9 plus 4 plus 1 plus 1 plus 1 plus 1 plus 9 and denominator 8 equals 3.25

Problem 2

mu equals the fraction with numerator 78 times 12 plus 80 times open paren 72 minus 12 close paren and denominator 72 equals 79.67 almost equals 79.7

Problem 3

p equals 100 minus open paren 40 plus 15 plus 12 plus 10 plus 15 close paren equals 8

n equals 8 over 40 times 120 equals 24

Problem 4

C sub 10 to the 14th power equals the fraction with numerator 14 factorial and denominator 10 factorial times 4 factorial equals 1001

Problem 5

why

mu equals 5

sigma equals the fraction with numerator the square root of 11 and denominator 2

Problem 6

1. down tack

2. up tack

3. down tack

4. down tack

Problem 7

A equals the 2 by 2 matrix Row 1: negative 2 negative 4 Row 2: 5 3

B equals the 2 by 2 matrix Row 1: negative 1 3 Row 2: 1 4

C equals the 2 by 2 matrix Row 1: 2 negative 1 Row 2: 4 2

D equals 2 times A minus B minus 3 C

D equals the 2 by 2 matrix Row 1: negative 4 negative 8 Row 2: 10 6 plus the 2 by 2 matrix Row 1: 1 negative 3 Row 2: negative 1 negative 4 plus the 2 by 2 matrix Row 1: negative 6 3 Row 2: negative 12 negative 6 equals the 2 by 2 matrix Row 1: negative 9 negative 8 Row 2: negative 3 negative 4

the absolute value of D equals 3 6 minus 24 equals 12

Problem 8

R equals the 2 by 2 matrix Row 1: 3 4 Row 2: 5 8 plus the 2 by 2 matrix Row 1: 0 negative 2 Row 2: 6 negative 1 equals the 2 by 2 matrix Row 1: 3 2 Row 2: 11 7

R to the negative 1 power equals 1 over negative 1 times the 2 by 2 matrix Row 1: 7 negative 2 Row 2: negative 11 3 equals the 2 by 2 matrix Row 1: negative 7 2 Row 2: 11 negative 3

Problem 9

A X equals B

X equals A to the negative 1 power times B

A to the negative 1 power equals one fifth times the 2 by 2 matrix Row 1: 3 1 Row 2: negative 2 1

X equals one fifth times the 2 by 2 matrix Row 1: 3 1 Row 2: negative 2 1 times the 2 by 2 matrix Row 1: negative 7 negative 3 Row 2: 11 4 equals the 2 by 2 matrix Row 1: Column 1, dot dot dot Column 2, dot dot dot Row 2: Column 1, dot dot dot Column 2, 2

Problem 10

the 2 by 2 matrix Row 1: negative 5 negative 7 Row 2: 2 6 minus 2 A equals the 2 by 2 matrix Row 1: negative 1 negative 3 Row 2: 4 10

the 2 by 2 matrix Row 1: negative 5 negative 7 Row 2: 2 6 minus the 2 by 2 matrix Row 1: 2 a 2 b Row 2: 2 c 2 d equals the 2 by 2 matrix Row 1: negative 1 negative 3 Row 2: 4 10

negative 5 minus 2 a equals negative 1

therefore a equals negative 2

negative 7 minus 2 b equals negative 3

therefore b equals negative 2

2 minus 2 c equals 4

therefore c equals negative 1

6 minus 2 d equals 10

therefore d equals negative 2

therefore the absolute value of A equals a d minus b c equals 4 minus 2 equals 2

Yippee!