Question

Ax=O Unique solution (trivial solution x-0) No free variables Infinitely many (nontrivial) solutions Some free variables Every column of A is pivot column | (=> rank(A) = # of columns of A Some columns of A are not pivot columns rank(A)< #of columns of A You can use the above figure to answer the following questions are about homogeneous systems Ax-0. Answer TRUE or FALSE. If the answer is FALSE, choose FALSE with the appropriate counterexample, i.e example that shows that the statement is FALSE. In the exam you'll have to justify your answers! If rank(A) # of columns of A, then the ho mogeneous system Choose. Ax-0 has only the trivial solution x = 0. Choose... FALSE (Counterexample: x+y= 0, 2x+2y=0, 3x+3y=0 has infinitly many solutions) FALSE (Counterexample: x+y+z=0, x-y+z=0 has non-trivial solutions) TRUE If rank(A) of columns of A, then the homogeneous system Ax-0 has infinitely many solutions. If a homogeneous system Ax-0 has non-trivial solutions, then Choose. necessarily rank(A) < # of rows of A If a homogeneous system Ax 0 has a non-zero solution x, then the Choose. system has infinitely many solutions.

Answer 1

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A homogeme ym netdy 6. han eith Axo Solurion TRUE Solumiom hank A Columms o A A 0 thiuie alekdn homegeneons yem TAUE A homo gen Conminent TRUE hand Hhen the dhiiar only homogenes yarem Ay o aluriom FALSE hn mom hui