Practice Problems on Methods to Find Rank of a Matrix

Problem 1: Find the rank of the matrix A = [Tex]\begin {bmatrix} 10 & 5\\ 6 & 0 \end {bmatrix}[/Tex] using minor method.

Problem 2: Find the rank of the matrix B = [Tex]\begin {bmatrix} 5 & 3\\ 2 & 4 \end {bmatrix}[/Tex] using echelon method.

Problem 3: Find the rank of the matrix X = [Tex]\begin {bmatrix} 1 & 5 & 6\\ 1 & 0 & 1\\ 1 & 3& 2 \end {bmatrix}[/Tex] using minor method.

Problem 4: Find the rank of the matrix D = [Tex] \begin {bmatrix} 7 & 0 & 0\\ 1 & 8 & 2\\ 0 & 4& 1 \end {bmatrix} [/Tex] using echelon method.

Problem 5: Find the rank of matrix F = [Tex] \begin {bmatrix} 2 & 4 & 2&4\\ 2 & 6 & 4&4\\ 4 & 8& 6&8\\ 6&14&8&12 \end {bmatrix} [/Tex] using normal form method.

To find the rank of a matrix find the highest order of the non-zero minor within the matrix. Rank of a matrix in the number that represents the number of non-zeros rows or columns in the matrix. If the rank of the matrix is r then the matrix contains at least one minor with order r and the minors with order greater than r is zero. The second method to find the rank of matrix is by converting it into Echelon form.

In this article we will discuss methods to find rank of a matrix in depth along with the rank definition, methods to find rank of a matrix i.e., by minors and by Echelon form. Also, we will discuss the properties of rank and solve some examples including both the methods. Let’s start our learning on the topic “Methods to Find Rank of a Matrix. “