1 1 1 0 1 1 0 0 1 Is this matrix bijective proveSolutionGive

1 1 1

0 1 1

0 0 1 Is this matrix bijective, prove

Solution

Given matrix is a square matrix. It\'s function maps 3x1 vectors into other 3x1 vectors. The matrix is not singular, meaning that all of its rows and columns are linearly independent.

So Ax=y implies that each value of y corresponds to 1 and only 1 value of x.

As the Augmented matrix for Ax=y has rank 3 same as rank of A.

That makes the Matrix both injective and surjective.