In Exercises 1 - 4,a. Give the order of each matrix,b. If A = [a_ij], identify a_32 and a_23, or explain why identification is not possible,1 - 5 π e0 7 - 6 - π- 2 1/2 11 - 1/5(please enclose the values above in a matrix symbol)

Verified step by step guidance

1. Identify the number of rows and columns in the matrix to determine its order. The matrix has 3 rows and 4 columns, so its order is 3x4.
2. Locate the element a_{32} in the matrix. This element is in the 3rd row and 2nd column, which is \( \frac{1}{2} \).
3. Locate the element a_{23} in the matrix. This element is in the 2nd row and 3rd column, which is \( -6 \).
4. Verify the positions of a_{32} and a_{23} by counting rows and columns to ensure accuracy.
5. Conclude that the matrix order is 3x4, a_{32} is \( \frac{1}{2} \), and a_{23} is \( -6 \).

Key Concepts

Matrix Order

The order of a matrix refers to its dimensions, expressed as the number of rows by the number of columns. For example, a matrix with 3 rows and 4 columns is said to be of order 3x4. Understanding the order is crucial for operations involving matrices, such as addition, multiplication, and determining compatibility for these operations.

Matrix Elements

Each entry in a matrix is referred to as an element, typically denoted as a_ij, where 'i' indicates the row number and 'j' indicates the column number. For instance, a_32 refers to the element in the 3rd row and 2nd column. Identifying specific elements is essential for performing calculations and understanding the structure of the matrix.

Matrix Notation

Matrix notation involves the use of brackets to enclose the elements of a matrix, which can include numbers, variables, or expressions. This notation helps in clearly defining the matrix and its elements, facilitating easier communication and understanding in mathematical contexts. Proper notation is vital for clarity in algebraic operations involving matrices.