**Matrix Theory**Consider the matrix \( A \):\[A = \begin{bmatrix}4 & 20 & 8 & -12 \\1 & 5 & 2 & -3 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\\end{bmatrix}\]**Objective:**Compute the following:1. Rank of \( A \)2. Nullity of \( A \)3. Sum of the rank and nullity of \( A \)**Formulas to use:**- **Rank of a Matrix**: The rank of a matrix is the maximum number of linearly independent row vectors in the matrix.- **Nullity of a Matrix**: Nullity is the dimension of the null space of the matrix, which is the number of solutions to the equation \( A \mathbf{x} = 0 \).- **Rank-Nullity Theorem**: This theorem states that the sum of the rank and nullity of a matrix \( A \) is equal to the number of columns of \( A \).**Enter your computations:**\[\begin{aligned}&\text{rank of } A = \quad \_\_\_\_\_ \\&\text{nullity of } A = \quad \_\_\_\_\_ \\&\text{rank of } A + \text{ nullity of } A = \quad \_\_\_\_\_ \\\end{aligned}\]**Visuals:**(Note: No graphs or diagrams are present in the image provided. Described computations need to be manually calculated based on the given matrix \( A \).)**Interactive Element:**Click the "Add Work" button to provide detailed steps of your computation (if available on the educational website interface).

Name: **Matrix Theory**Consider the matrix \( A \):\[A = \begin{bmatrix}4 &
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: **Matrix Theory**Consider the matrix \( A \):\[A = \begin{bmatrix}4 & 20 & 8 & -12 \\1 & 5 & 2 & -3 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\\end{bmatrix}\]**Objective:**Compute the following:1. Rank of \( A \)2. Nullity of \( A \)3. Sum of the rank and nu