a. Give the order of each matrix.


b. If A = [aᵢⱼ] , identify a₃₂ and a₂₃, or explain why identification is not possible.
$\begin{bmatrix}1 & -5 & \pi & e \\0 & 7 & -6 & -\pi \\-2 & \frac{1}{2} & 11 & -\frac{1}{5}\end{bmatrix}$

Verified step by step guidance

1. Step 1: Identify the order of the matrix by counting the number of rows and columns. The matrix has 3 rows and 4 columns, so its order is \$3 \times 4$.
2. Step 2: Understand the notation \(A = [a_{ij}]\), where \(a_{ij}\) represents the element in the \(i^{th}\) row and \(j^{th}\) column of matrix \(A\).
3. Step 3: To find \(a_{32}\), locate the element in the 3rd row and 2nd column of the matrix. This corresponds to the value \(\frac{1}{2}\).
4. Step 4: To find \(a_{23}\), locate the element in the 2nd row and 3rd column of the matrix. This corresponds to the value \(-6\).
5. Step 5: Summarize the findings: The order of the matrix is \$3 \times 4\(, \)a_{32} = \frac{1}{2}\(, and \)a_{23} = -6$.

Key Concepts

Matrix Order

The order of a matrix is defined by the number of its rows and columns, expressed as 'rows × columns'. It helps in identifying the size and structure of the matrix, which is essential for performing operations like addition, multiplication, or finding specific elements.

Matrix Element Notation (a_ij)

In matrix notation, a_ij represents the element located in the i-th row and j-th column of matrix A. Understanding this notation is crucial for identifying or manipulating specific elements within the matrix, such as a_32 (3rd row, 2nd column) or a_23 (2nd row, 3rd column).

Matrix Representation and Interpretation

A matrix is typically enclosed in brackets and contains elements arranged in rows and columns. Interpreting the matrix correctly, including recognizing special values like π or fractions, is important for accurate identification of elements and understanding the matrix's properties.