library(glmnet)
set.seed(65587)
x <- matrix(rnorm(100), 25, 4)
#x <- as.data.frame(x)
#colnames(x) <- c('x1', 'x2', 'x3', 'x4')

y1 <- 0.9*x[,1] + 0.00*x[,2] + 1.2*x[,3] + 0.3*x[,4]
y2 <- 1.1*x[,1] + 0.02*x[,2] + 0.8*x[,3] + 0.4*x[,4]
y3 <- 0.9*x[,1] + 0.01*x[,2] + 1.3*x[,3] + 0.5*x[,4]
y <- cbind(y1, y2, y3)
mfit = glmnet(x, y, family = "mgaussian")
plot(mfit,type.coef="2norm", label = TRUE)

Extract coefficients at a single value of lambda.

coef(mfit, s=1)  
## $y1
## 5 x 1 sparse Matrix of class "dgCMatrix"
##                     1
## (Intercept) 0.1288243
## V1          0.5088899
## V2          .        
## V3          0.7053134
## V4          .        
## 
## $y2
## 5 x 1 sparse Matrix of class "dgCMatrix"
##                     1
## (Intercept) 0.1443105
## V1          0.5745998
## V2          .        
## V3          0.5525302
## V4          .        
## 
## $y3
## 5 x 1 sparse Matrix of class "dgCMatrix"
##                     1
## (Intercept) 0.1301095
## V1          0.5149819
## V2          .        
## V3          0.7736209
## V4          .
coef(mfit, s=0.1)  
## $y1
## 5 x 1 sparse Matrix of class "dgCMatrix"
##                      1
## (Intercept) 0.01255091
## V1          0.86321564
## V2          .         
## V3          1.14735011
## V4          0.26789238
## 
## $y2
## 5 x 1 sparse Matrix of class "dgCMatrix"
##                      1
## (Intercept) 0.01461891
## V1          1.04740569
## V2          .         
## V3          0.77978597
## V4          0.35457122
## 
## $y3
## 5 x 1 sparse Matrix of class "dgCMatrix"
##                      1
## (Intercept) 0.01234107
## V1          0.86660998
## V2          .         
## V3          1.24301940
## V4          0.44445080
coef(mfit, s=0.001)
## $y1
## 5 x 1 sparse Matrix of class "dgCMatrix"
##                       1
## (Intercept) 0.006957324
## V1          0.879686389
## V2          .          
## V3          1.170550691
## V4          0.282269463
## 
## $y2
## 5 x 1 sparse Matrix of class "dgCMatrix"
##                      1
## (Intercept) 0.00792238
## V1          1.07340039
## V2          .         
## V3          0.78606260
## V4          0.37622367
## 
## $y3
## 5 x 1 sparse Matrix of class "dgCMatrix"
##                      1
## (Intercept) 0.00672596
## V1          0.88298571
## V2          .         
## V3          1.26665282
## V4          0.46996604

According to the result, x2 is never chosen. When regulation is large, x4 is also not chosen. x1 and x3 are cosidered to be important.