Exercise · ZW-MATRIX-RANK-005 · ★☆☆ Basic
Compute the rank of \(\begin{pmatrix}1&2&3\\4&5&6\\7&8&9\end{pmatrix}\).
Choose one option.
Show answer
- B. 2
Explanation
Row reducing, \(R_2-4R_1=(0,-3,-6)\) and \(R_3-7R_1=(0,-6,-12)\); the third is twice the second and vanishes. There are 2 pivots: rank 2.
Review the concept: Rank of a matrix
The rank of a matrix \(A\) is the dimension of the subspace spanned by its columns.
\[\operatorname{rank}(A)=\dim\operatorname{col}(A)\]
More practice problems: rank of a matrix
- ZW-MATRIX-RANK-001 What is the rank of [1 2; 2 4]?
- ZW-MATRIX-RANK-002 What is the rank of the identity matrix I_3?
- ZW-MATRIX-RANK-003 What is the largest possible rank of a 3× 5 matrix?
- ZW-MATRIX-RANK-004 What is the rank of the 2× 2 zero matrix?
- ZW-MATRIX-RANK-006 Compute the rank of [1 0 2; 0 1 3; 1 1 5].
- ZW-MATRIX-RANK-007 At most how many linearly independent rows does A=[1 2 0 1; 0 0 1 3; 1 2 1 4] have?
- ZW-MATRIX-RANK-008 A 4× 4 matrix A has rank 3. Which statement is true?
- ZW-MATRIX-RANK-009 Compute the rank of [1 2 1; 2 4 3; 1 2 2].