Inverse Matrix Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Does [6342]\begin{bmatrix} 6 & 3 \\ 4 & 2 \end{bmatrix} have an inverse? Explain.

Solution

  1. 1
    detโก=6(2)โˆ’3(4)=12โˆ’12=0\det = 6(2) - 3(4) = 12 - 12 = 0.
  2. 2
    Since detโก=0\det = 0, the matrix is singular and has no inverse.

Answer

No, the determinant is 00.
A matrix is invertible iff detโกโ‰ 0\det \neq 0. Here the rows are proportional ([6,3]=1.5ร—[4,2][6,3] = 1.5 \times [4,2]), meaning the matrix maps all inputs onto a line โ€” information is lost and cannot be recovered.

About Inverse Matrix

The inverse of a square matrix AA, written Aโˆ’1A^{-1}, is the unique matrix such that AAโˆ’1=Aโˆ’1A=IAA^{-1} = A^{-1}A = I (the identity matrix). A matrix has an inverse if and only if its determinant is nonzero.

Learn more about Inverse Matrix โ†’

More Inverse Matrix Examples

Example 1 medium

Find the inverse of [formula].

Example 2 easy

Find the inverse of [formula].

Example 3 easy

Find the inverse of [formula].

โ† All Inverse Matrix Examples Inverse Matrix Concept