题目

knitr::include_graphics("c:/dytjfx/problem.png")

机算

## 定义协方差矩阵 Sigma

Sigma <- matrix(c(9, 1, -2,
                   1, 20, 3,
                   -2, 3, 12), nrow = 3, byrow = TRUE)

## 定义变换矩阵 A
A <- matrix(c(2, 3, 1,
               1, -2, 5,
               0, 1, -1), nrow = 3, byrow = TRUE)

## 计算 y 的协方差矩阵
Cov_y <- A %*% Sigma %*% t(A)

## 输出结果
print(Cov_y)
##      [,1] [,2] [,3]
## [1,]  250  -26   48
## [2,]  -26  305  -76
## [3,]   48  -76   26

笔算

knitr::include_graphics("C:/dytjfx/solve.jpg")