Suppose p(λ) = λ(λ−1)(λ+2)(λ+1) is the characteristic polynomial of a matrix a. consider the statements:
i: a must be a 4 × 4 matrix.
ii: a can be diagonalized.
iii: a is invertible.
which of the statements i, ii, and iii are false?

 The false statement is

III. A is invertible.

Step-by-step explanation:  Given that the characteristic polynomial of a matrix A is

We are to select the statement that is FALSE.

The characteristic values of A are given by

.

I. The characteristic polynomial of A has degree 4, so the order of A is 4. That is, the matrix A must be a 4 × 4 matrix.

So, the statement I is true.

II. Since all the characteristic values of A are all distinct, so there will be 4 linearly independent characteristic vectors.

Therefore, there exists an invertible matrix P such that where D is daigonal with characteristic values as diagonal matrix.

This makes A diagonalizable.

So, the statement II is TRUE.  

III. We know that the determinant of a matrix is equal to the product of the characteristic values of the matrix.

Therefore,

This implies that A is non-invertible.

So, statement III is FALSE.

Thus, statement III is FALSE.

2

step-by-step explanation:

95.03 is the answer. hope this !