If the columns of matrix A are linearly independent, then the only solution of Ax = 0 is the trivial solution.

Yes, this statement is **true**.

Here’s why:

When the columns of matrix \( A \) are **linearly independent**, it means that there are no nontrivial linear combinations of the columns of \( A \) that result in the zero vector. In other words, the only way to express the zero vector as a linear combination of the columns of \( A \) is by assigning a zero coefficient to each of the columns.

Mathematically, this

Explore why the solution to Ax = 0 is only the trivial solution when the columns of matrix A are linearly independent. This problem covers essential concepts in linear algebra, such as matrix theory and linear independence, suitable for college-level or advanced high school students.

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