问题描述
我是新的矩阵世界，对于这个基本问题，我无法想像：
I am new to world of matrix, sorry for this basic question I could not figure out:
我有四个矩阵（一个未知）。
I have four matrix (one unknown).
矩阵X
x <- c(44.412, 0.238, -0.027, 93.128, 0.238, 0.427, -0.193, 0.673, 0.027,
-0.193, 0.094, -0.428, 93.128, 0.673, -0.428, 224.099)
X <- matrix(x, ncol = 4 )
矩阵B：需要解决，1 X 4（列x nrows）与b1，b2，b3，b4值
Matrix B : need to be solved , 1 X 4 (column x nrows), with b1, b2, b3, b4 values
Matrix G
g <- c(33.575, 0.080, -0.006, 68.123, 0.080, 0.238, -0.033, 0.468, -0.006,
-0.033, 0.084, -0.764, 68.123, 0.468, -0.764, 205.144)
G <- matrix(g, ncol = 4)
Matrix A
a <- c(1, 1, 1, 1) # one this case but can be any value
A <- matrix(a, ncol = 1)
解决方案：
B = inv(X) G A # inv(X) is inverse of the X matrix multiplied by G and A
我不知道如何正确地解决这个问题，特别是矩阵。感谢你的帮助。
I did not know how to solve this properly, particularly inverse of the matrix. Appreciate your help.
推荐答案
我猜猜，Nick和Ben都是老师，比做别人的作业要大得多但是，完整解决方案的道路真的非常明显，在下一步中没有什么意义：
I'm guessing that Nick and Ben are both teachers and have even greater scruples than I do about doing other peoples' homework, but the path to a complete solution was really so glaringly obvious that it didn't make a lot of sense not to tae the next step:
B = solve(X) %*% G %*% A
> B
[,1]
[1,] -2.622000509
[2,] 7.566857261
[3,] 17.691911600
[4,] 2.318762273
可以通过提供一个身份矩阵作为第二个参数来调用QR方法：
The QR method of inversion can be invoked by supplying an identity matrix as the second argument:
> qr.solve(G, diag(1,4))
[,1] [,2] [,3] [,4]
[1,] 0.098084556856 -0.0087200426695 -0.3027373205 -0.0336789016478
[2,] -0.008720042669 4.4473233701790 1.7395207242 -0.0007717410073
[3,] -0.302737320546 1.7395207241703 13.9161591761 0.1483895429511
[4,] -0.033678901648 -0.0007717410073 0.1483895430 0.0166129089935
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