Math Problem Statement

Use technology to find the inverse of the given matrix (when it exists). Round all entries in your answer to two decimal places. (Caution: Because of rounding errors, technology sometimes produces an "inverse" of a singular matrix. These often can be recognized by their huge entries. If the inverse doesn't exist, enter DNE in any cell of the matrix.)

−0.2 −0.1 −0.2

2.2 1.1 2.2 −0.3 0.9 −5.1

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Inverses
Determinants

Formulas

Matrix Inverse Formula: A^(-1) = (1/det(A)) * adj(A)
Determinant of 3x3 Matrix: det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)

Theorems

Inverse Matrix Theorem: A matrix is invertible if and only if its determinant is non-zero

Suitable Grade Level

Grades 10-12, College level