Find the Rank [[-4,1],[5,6]]

Problem

rank(−4)

Solution

1. Identify the matrix A and its dimensions.

A=[[−4,1],[5,6]]

The matrix is a 2×2 square matrix.

2. Calculate the determinant of the matrix to check if it is non-singular.

det(A)=(−4)*(6)−(1)*(5)

det(A)=−24−5

det(A)=−29

3. Determine the rank based on the determinant.
   Since det(A)≠0 the rows and columns are linearly independent.
   For an n×n matrix, if the determinant is non-zero, the rank is n

Final Answer

rank(−4)=2

Want more problems? Check here!