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Special Types of Matrices

  • Thread starter hkus10
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  • #1
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1) show that if AB = AC and A is nonsingular, then B = C.

2) show that if A is nonsingular and AB = 0 for an n x n matrix B, then B = 0.

3) Consider the homogenous system Ax=0, where A is n x n. If A is nonsingular, show that the only solution is the trivial one, x=0.

4) Prove that if A is symmetric and nonsingular, then A^-1 is symmetric.

Please help and show all your work or at least give me some directions!

Thanks
 

Answers and Replies

  • #2
HallsofIvy
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What does your textbook say "nonsingular" means for a matrix? What does your text book say about "invertible"?
 
  • #3
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What does your textbook say "nonsingular" means for a matrix? What does your text book say about "invertible"?
An n x n matrix A is called nonsingular, or invertible, if there exists an n x n matrix B such that AB = BA = In; such a B is called inverse of A.
 
  • #4
Dick
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An n x n matrix A is called nonsingular, or invertible, if there exists an n x n matrix B such that AB = BA = In; such a B is called inverse of A.
Ok, use that. You usually write the inverse of A as A^(-1). Multiply both sides of AB=AC by A^(-1).
 

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