Matrix Rank Worksheet
1Calculate the rank of the matrix
2Calculate the rank of the matrix by the gaussian elimination method.
3Calculate the rank of the matrix by the gaussian elimination method.
4Calculate the rank of the matrix by determinants.
5Calculate the rank of the matrix by determinants.
6Calculate the rank of the matrix by determinants.
7Calculate the rank of the matrix by determinants.
1
Calculate the rank of the matrix.
r3 = 2r1
r4 is null
r5 = 2r2 + r1
r(A) = 2.
2
Calculate the rank of the matrix by the gaussian elimination method.
r1 - 2 r2
r3 - 3 r2
r3 + 2 r1
Therefore r(A) =2.
3
Calculate the rank of the matrix by the gaussian elimination method.
r2 = r2 − 3r1
r3= r3 − 2r1
r(A) = 3.
4
Calculate the rank of the matrix by determinants.
|2|=2 ≠0
r(A) = 2
5
Calculate the rank of the matrix by determinants.
r(B) = 4
6
Calculate the rank of the matrix by determinants.
Remove the third column as it is zero, the fourth because it is proportional to the first and the fifth because it is the linear combination of the first and second: c5 = −2 · c1 + c2
r(C) = 2
7
Calculate the rank of the matrix by determinants.
c3 = c1 + c2
|2|=2≠0
r(D) = 2
