If x is a nontrivial solution of Ax=0, then every entry in x is nonzero.Is the statement true or false?
The statement is false
The statement is false.
A nontrivial solution of Ax=0 means that there exists a vector x which is not the zero vector, such that when multiplied by the matrix A, the resulting vector is the zero vector.
In other words, Ax=0 implies that there is at least one entry in vector x that is nonzero.
However, this does not mean that every entry in x is nonzero. It is possible to have some entries in x equal to zero while still satisfying the equation Ax=0.
Therefore, the statement is false.
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