4. hét

## I.   x + 2y -  z = 8
## II.  2x + 3y +  z = 10
## III. 3x + 5y + 2z = 16
 
b <- rbind(c(1, 2, -1), c(2, 3, 1), c(3, 5, 2))
j <- c(8, 10, 16)
solve(b, j)
 
## I.   x + 2y + 3z = 1
## II.  4x + 5y + 6z = 2
## III. 7x + 8y + 9z = 3
 
b <- rbind(c(1, 2, 3), c(4, 5, 6), c(7, 8, 9))
j <- 1:3
solve(b, j)

m <- b
library(scatterplot3d)
scatterplot3d(m, color = "red", pch = 19, cex.symbols = 5)

b <- cbind(c(2, 0, 0), c(0, 2, 0), c(0, 0, 2))
solve(b, m)
solve(b) %*% m
 
## vizuálisan
scatterplot3d(solve(b, m), color = "red", pch = 19, cex.symbols = 5)

m <- rbind(c(1, 1), c(4, 4), c(4, 1), c(1, 4))
plot(m)
 
b <- rbind(c(0.5, 0), c(0, 3))
solve(b, t(m))
plot(t(solve(b, t(m))))
plot(t(solve(b, t(m))), xlim = c(0, 10), ylim = c(0, 10))
plot(m, xlim = c(0, 10), ylim = c(0, 10))
 
## egy ábrán
plot(m, xlim = c(0, 10), ylim = c(0, 10))
points(t(solve(b, t(m))), col = "red")