Math Problem Statement
Determine if A is invertible and, if so, compute A−1. (If the answer does not exist, enter DNE in any cell of the matrix.) A =
4 5 7
−1 −2 −5 −1 −1 0 A−1 = 5/2 7/2 5/2
-5/2 -7/2 -7/2 1/2 1/2 1/2
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Inverses
Determinants
Formulas
Determinant of a 3x3 matrix: det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)
Inverse of a matrix: A^{-1} = 1/det(A) * adj(A)
Theorems
Matrix Invertibility Theorem
Determinant Theorem
Suitable Grade Level
Grades 11-12, College