For Problems 33-34, use properties of the inverse to prove the given statement. 33. If A is an nxn invertible skew-symmetric matrix, then skew-symmetric. A-¹ is -1 34. If A is an n x n invertible symmetric matrix, then A-¹ is symmetric. 35. Let A be an n × n matrix with A¹² = 0. Prove that In - A³ is invertible with 3 (In − A³)−¹ = In + A³ + Aº + Aº. 3 6
For Problems 33-34, use properties of the inverse to prove the given statement. 33. If A is an nxn invertible skew-symmetric matrix, then skew-symmetric. A-¹ is -1 34. If A is an n x n invertible symmetric matrix, then A-¹ is symmetric. 35. Let A be an n × n matrix with A¹² = 0. Prove that In - A³ is invertible with 3 (In − A³)−¹ = In + A³ + Aº + Aº. 3 6
Chapter7: Systems Of Equations And Inequalities
Section7.7: Solving Systems With Inverses
Problem 1SE: In a previous section, we showed that matrix multiplication is not commutative, that is, ABBA in...
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