A generic $$ \boldsymbol{n} imes \boldsymbol{n} $$ system of linear equations can have zero solutions, one solution, or an infinite number of solutions. It will have exactly one unique solution if and only if the determinant of its coefficient matrix is Select an answer $$ \vee $$ A homogeneous system either has exactly one solution or it has an infinite number of solutions. In either case, a homogenous system always has at least one solution, the where all values are 0 . $$ \square $$ Select an answer sotution An $$ \boldsymbol{n} imes \boldsymbol{n} $$ homogeneous system has a infinite number of $$ \square $$ Select an answer $$ \checkmark $$ solutions if and only if its determinant is $$ \square $$ Select an answer . Question Help: Video Submit Question

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A generic $$ \boldsymbol{n} 	imes \boldsymbol{n} $$ system of linear equations can have zero solutions, one solution, or an infinite number of solutions. It will have exactly one unique solution if and only if the determinant of its coefficient matrix is Select an answer $$ \vee $$ A homogeneous system either has exactly one solution or it has an infinite number of solutions. In either case, a homogenous system always has at least one solution, the where all values are 0 . $$ \square $$ Select an answer sotution An $$ \boldsymbol{n} 	imes \boldsymbol{n} $$ homogeneous system has a infinite number of $$ \square $$ Select an answer $$ \checkmark $$ solutions if and only if its determinant is $$ \square $$ Select an answer . Question Help: Video Submit Question

UpStudy AI · Accepted Answer

1. For a generic $$ n \times n $$ system to have exactly one unique solution, the determinant of the coefficient matrix must be nonzero, i.e., 
   $$
   \det(A) \neq 0.
   $$

2. A homogeneous system always has at least one solution (the trivial solution where all variable values are $$0$$), and it either has exactly one solution or infinitely many solutions.

3. An $$ n \times n $$ homogeneous system has an infinite number of solutions if and only if the determinant of its coefficient matrix is zero, i.e., 
   $$
   \det(A) = 0.
   $$
For a generic $$ n \times n $$ system to have exactly one unique solution, the determinant of the coefficient matrix must be nonzero. A homogeneous system always has at least one solution (the trivial solution where all variables are zero) and either has exactly one solution or infinitely many solutions. An $$ n \times n $$ homogeneous system has infinitely many solutions if and only if the determinant of its coefficient matrix is zero.

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