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Error in solve.default(mat)  Lapack routine dgesv system is exactly singular:  Lapack routine dgesv: system is exactly singular: U[2,2] = 0

When attempting to utilize the solution() method on a singular matrix that lacks a matrix inverse, an error like this one will appear.

This lesson explains how to fix this mistake practically.

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Let’s say we use R to build the matrix shown below.

Let’s create a singular matrix

mat <- matrix(c(1, 1, 1, 1), ncol=2, nrow=2)

Now we can view the matrix

mat
     [,1] [,2]
[1,]    1    1
[2,]    1    1

Now imagine that we try to compute the matrix inverse using the solution() function.

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invert matrix try

solve(mat)
Error in solve.default(mat) :  Lapack routine dgesv: system is exactly singular: U[2,2] = 0

The absence of an inverse matrix in the matrix we generated results in an error.

Please have a look at this Wolfram MathWorld article that provides ten examples of matrices without inverse matrices.

A matrix is considered singular by definition if its determinant is zero.

Before attempting to invert a particular matrix, you can find its determinant using the det() function:

Let’s compute the matrix’s determinant

det(mat)
[1] 0

Our matrix’s determinant is zero, which explains why we encounter a problem.

How to correct the issue

Simply making a matrix that is not single is the only way to correct this issue.

Consider using R’s solution() function to invert the matrix shown below:

Now we can generate a non-singular matrix

mat <- matrix(c(1, 7, 4, 2), ncol=2, nrow=2)

let’s view the matrix

mat
     [,1] [,2]
[1,]    1    4
[2,]    7    2

Now we can calculate the determinant of the matrix.

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det(mat)
[1] -26

Let’s try to invert the matrix

solve(mat)
            [,1]        [,2]
[1,] -0.07692308  0.15384615
[2,]  0.26923077 -0.03846154

The matrix is not singular, so when we invert it we don’t encounter any errors.

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