#3Please answer a, b and c ### Matrix Determinant CalculationConsider the following matrix \( A \):\[ A = \begin{bmatrix}2 & 1 & -1 & 0 \\2 & 0 & 3 & 0 \\1 & -1 & 0 & 4 \\0 & 3 & 2 & 2\end{bmatrix} \]#### Part (a): Compute the Determinant by DefinitionCompute the determinant of the matrix \(A\) using the definition. This involves writing out all the permutations of the matrix elements and calculating the sum of all the products, considering their signs.#### Part (b): Compute the Determinant by Row-ReducingCompute the determinant by reducing the matrix \(A\) to a triangular form using row operations. The determinant of a triangular matrix is the product of its diagonal elements. Note that remember to keep track of any row swaps, as each row swap changes the sign of the determinant.#### Part (c): Compute the Determinant using Cofactor Expansion Compute the determinant a third time using cofactor expansion along column 3. This involves selecting a row (or column), expanding the determinant across that row (or column), and summing the products of the elements and their corresponding minors, each multiplied by \((-1)^{i+j}\), where \(i\) is the row index and \(j\) is the column index of the element.Ensure that your answers for parts (a), (b), and (c) are consistent.

Name: #3Please answer a, b and c ### Matrix Determinant CalculationConsider
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: #3Please answer a, b and c ### Matrix Determinant CalculationConsider the following matrix \( A \):\[ A = \begin{bmatrix}2 & 1 & -1 & 0 \\2 & 0 & 3 & 0 \\1 & -1 & 0 & 4 \\0 & 3 & 2 & 2\end{bmatrix} \]#### Part (a): Compute the Determinant by Definiti