> x = c(1,0,2)
> y=c(3,1,2)
> lm(y~x)

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
        1.5          0.5  

> mod = lm(y~x)
> mod

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
        1.5          0.5  

> summary(mod)

Call:
lm(formula = y ~ x)

Residuals:
   1    2    3 
 1.0 -0.5 -0.5 

Coefficients:
            Estimate Std. Error t value
(Intercept)    1.500      1.118   1.342
x              0.500      0.866   0.577
            Pr(>|t|)
(Intercept)    0.408
x              0.667

Residual standard error: 1.225 on 1 degrees of freedom
Multiple R-squared:  0.25,	Adjusted R-squared:  -0.5 
F-statistic: 0.3333 on 1 and 1 DF,  p-value: 0.6667 

> x2 = x^2
> lm(y~x+x^2)

Call:
lm(formula = y ~ x + x^2)

Coefficients:
(Intercept)            x  
        1.5          0.5  

> lm(y~x+x2)

Call:
lm(formula = y ~ x + x2)

Coefficients:
(Intercept)            x           x2  
        1.0          3.5         -1.5  

> A = matrix(c(1,2,3,4,5,6),3,2)
> A
     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6
> B = matrix(rep(3,6),2,3)
> B
     [,1] [,2] [,3]
[1,]    3    3    3
[2,]    3    3    3
> A%*%B
     [,1] [,2] [,3]
[1,]   15   15   15
[2,]   21   21   21
[3,]   27   27   27
> A*B
Error in A * B : non-conformable arrays
> C = matrix(rnorm(6),2,3)
> C
           [,1]        [,2]      [,3]
[1,] -0.6314838 -0.02117242 1.2428954
[2,] -1.6265466  1.40916533 0.1642478
> B*C
          [,1]        [,2]      [,3]
[1,] -1.894451 -0.06351725 3.7286862
[2,] -4.879640  4.22749600 0.4927435
> C = matrix(rbinom(6,5,.5),2,3)
> C
     [,1] [,2] [,3]
[1,]    2    1    3
[2,]    3    2    4
> B
     [,1] [,2] [,3]
[1,]    3    3    3
[2,]    3    3    3
> B*C
     [,1] [,2] [,3]
[1,]    6    3    9
[2,]    9    6   12
> solve(t(C)%*%C)
Error in solve.default(t(C) %*% C) : 
  system is computationally singular: reciprocal condition number = 6.20003e-18
> C=matrix(rnorm(9),3,3)
> C
           [,1]      [,2]      [,3]
[1,] -0.6941833 0.7670638 1.3231382
[2,]  0.2784828 0.2658453 0.1140798
[3,] -0.1424353 0.9918065 0.2311486
> solve(C)
           [,1]       [,2]       [,3]
[1,] -0.1326884 2.91322806 -0.6782448
[2,] -0.2069304 0.07187407  1.1490360
[3,]  0.8061280 1.48675505 -1.0219720
> ?rnorm
starting httpd help server ... done
> C=matrix(rnorm(9),3,3)
> C
            [,1]        [,2]       [,3]
[1,] -0.02481775  0.35129724  1.0170294
[2,] -0.01964760 -1.24171454 -0.1344481
[3,]  0.72518964  0.03616592  0.3254510
>