Question

under what condition the rank of the matrix greater than 3​

Answer 1

Answer:

Matrix A has only one linearly independent row, so its rank is 1. Hence, matrix A is not full rank. Now, look at matrix B. All of its rows are linearly independent, so the rank of matrix B is 3.

Answer 2

Answer:

Matrix A has only one linearly independent row, so its rank is 1. Hence, matrix A is not full rank. Now, look at matrix B. All of its rows are linearly independent, so the rank of matrix B is 3.

Step-by-step explanation:

Note that A is an invertible matrix if and only if its rank is 3. Therefore the (3,3)-entry of the last matrix must be nonzero: k2−3k+2=(k−1)(k−2)≠0. It follows that the matrix A is invertible for any k except k=1,2.

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