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https://github.com/szymon-jozef/ZUT-notatki.git
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98 lines
1.5 KiB
R
98 lines
1.5 KiB
R
# zad 1
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# a)
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(2 * 3^3)/(sin(pi/6)) + log(2401,7) # 112
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# b)
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abs(-9 + 5^-3) + (2^(1/3))^(1/5) # 10.03929
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# c)
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2^(1/3) * log((3^5 + 5^2 - 12),2) + (3 + (7^(4/3)))^(1/5) # 10.03929
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# zad 2
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a = c(1,-10,12,3,2,1,-8,4,5)
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A = matrix(a, 3, 3)
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b = c(1,3,-1,2,1,5)
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B = matrix(b,3, 2)
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# a)
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det(A) # 572
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# b)
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solve(A)
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#[,1] [,2] [,3]
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#[1,] 0.01048951 -0.04020979 0.04895105
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#[2,] 0.17132867 0.17657343 0.13286713
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#[3,] -0.05944056 0.06118881 0.05594406
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# c)
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t(A)
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#[,1] [,2] [,3]
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#[1,] 1 -10 12
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#[2,] 3 2 1
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#[3,] -8 4 5
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# d)
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A%*%B
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# [,1] [,2] [,3]
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#[1,] 1 -10 12
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#[2,] 3 2 1
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#[3,] -8 4 5
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A%*%t(A)
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#[,1] [,2] [,3]
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#[1,] 74 -36 -25
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#[2,] -36 120 -98
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#[3,] -25 -98 170
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A%*%A
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#[,1] [,2] [,3]
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#[1,] -125 1 -36
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#[2,] 18 -22 108
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#[3,] 62 43 -67
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# e)
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A[1,] * B[,2]
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# [1] 2 3 -40
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# zad 3 na kolokwium
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c = c(1,2,5,-2,1,2,5,-3,-1,0,2,1,-2,3,5,2)
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C = matrix(c, 4, 4)
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D = c(-7,21,40,2)
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solve(C,D)
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# [1] 1 2 0 5
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solve(C)[2,3]
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# [1] -0.1578947
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# zad 4 na kolokwium
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w = (1:100)^2
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summary.factor(w%%10)
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# 0 1 4 5 6 9
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# 10 20 20 10 20 20
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summary.factor(w%%2 == 0)
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# FALSE TRUE
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# 50 50
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summary.factor(w%%3 == 0)
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# FALSE TRUE
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# 67 33
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summary.factor(w%%3 == 0 & w%%2 == 0)
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# FALSE TRUE
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# 84 16
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# zad 5 na kolokwium
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w = seq(21,29903, by=7)^3
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summary.factor(w %% 100 == 23)
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#FALSE TRUE
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# 4226 43
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# zad 6
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