Question

Find the rank of the matrix:

[25 −3 −4]
[69 −5 −2]


A. 2
B. 1
C. 0
D. 3

Answer 1

The rank of the given matrix is a)2.

Step-by-step explanation:

The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. To find the rank of the given matrix:

1. First, you need to write the matrix in row-echelon form or reduced row-echelon form.
2. Then, count the number of non-zero rows in the row-echelon form or reduced row-echelon form. This will give you the rank of the matrix.

Let's find the rank of the given matrix:

[25 -3 -4]
[69 -5 -2]

By performing row operations, we can reduce the matrix to row-echelon form:
[1 0 -2/59]
[0 1 -5/59]

Since there are 2 non-zero rows in the row-echelon form, the rank of the matrix is a) 2.