Practice Problems on Rank of 3×3 Matrix
Q1. Find the rank of 3×3 matrix A = [Tex]\begin{bmatrix} 1&4&-2\\ 5&1&3\\ 7&0&8 \end {bmatrix}[/Tex] using Minor method.
Q2. Calculate the rank of 3×3 matrix B = [Tex]\begin{bmatrix} -10&0&1\\ 6&20&-5\\ -2&3&30 \end {bmatrix}[/Tex] using minor method.
Q3. Find the rank of 3×3 matrix C = [Tex]\begin{bmatrix} 3&-8&6\\ 5&-1&-7\\ -2&10&0 \end {bmatrix}[/Tex] using Echelon Form.
Q4. Calculate the rank of 3×3 matrix D = [Tex]\begin{bmatrix} -1&8&15\\ 3&2&25\\ 4&26&-5 \end {bmatrix}[/Tex] using Echelon Form.
Q5. Find the rank of 3×3 matrix X = [Tex]\begin{bmatrix} 4&0&-2\\ 9&1&3\\ 14&7&21 \end {bmatrix}[/Tex] using normal form.
Q6. Calculate the rank of 3×3 matrix Y = [Tex]\begin{bmatrix} 1&-5&3\\ 2&9&4\\ 10&12&7 \end {bmatrix}[/Tex] using normal form.
How to Find Rank of a 3×3 Matrix
Rank of a matrix is equal to the number of linear independent rows or columns in it. The rank of the matrix is always less than or equal to the order of the matrix.
In this article we will explore how to find rank of 3×3 matrix in detail along with the basics of the rank of a matrix.
Table of Content
- What is Rank of a Matrix?
- How to Find Rank of a 3×3 Matrix
- Solved Examples on Rank of 3×3 Matrix
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