Thank you for sharing the image! Let’s break this down step by step to solve each section of the questions provided in the image. Here’s how I will proceed:

Question 3: Classify matrices

We need to classify each matrix as symmetric, skew-symmetric, diagonal, scalar, upper triangular, or lower triangular:

• Symmetric: $A = A^T$
• Skew-symmetric: $A = -A^T$
• Diagonal: All off-diagonal entries are zero.
• Scalar: Diagonal matrix with all diagonal entries equal.
• Upper triangular: All elements below the main diagonal are zero.
• Lower triangular: All elements above the main diagonal are zero.

Question 4: Reduced Row Echelon Form (RREF)

We’ll use Gaussian elimination to transform the matrices into their reduced row echelon form.

Question 5: Solve Systems of Linear Equations

We’ll apply the Gaussian Elimination method to solve the given systems.

Question 6: Matrix Inverses

For each matrix, we’ll compute the inverse using the formula or row reduction if the determinant is non-zero. For $2 \times 2$ matrices, the inverse is: $A^{-1} = \frac{1}{\det(A)} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$ where $\det(A) = ad - bc$.

For larger matrices, row reduction is used.

Question 7: Milk Mixture Problem

This is a system of linear equations. Let:

• $x$: Amount of 20% butterfat milk
• $y$: Amount of 15% butterfat milk

We’ll solve the system to satisfy both total volume and butterfat percentage.

Would you like me to start with a specific section, or should I work through them in order? Let me know!