Question

“If A is a 3×4 matrix, then the transformation x→Axis one-to-one.” The statement is true of false? explain your answer

Answer 1

Solution: “If A is a 3×4 matrix, then the transformation x→Axis one-to-one.”. This statement is False.

Explanation: If T: Rn→Rm is a matrix linear transformation. that is a matrix have m rows and n columns. The transformation will be one to one if each row and each column can only contain one pivot, so in order for A to have a pivot in every column, n ≤ m. But here number of columns is greater than number of rows. Hence, transformation x → Ax is not one-to-one.