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,4 - 7 5- 6 8 - 1(please enclose the values above in a matrix symbol)

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1. Identify the number of rows and columns in the matrix to determine its order.
2. The matrix has 2 rows and 3 columns, so its order is 2x3.
3. Identify the element a_{32}, which is in the 3rd row and 2nd column. Since the matrix has only 2 rows, a_{32} does not exist.
4. Identify the element a_{23}, which is in the 2nd row and 3rd column. The element in this position is -1.
5. Conclude that a_{32} cannot be identified because the matrix does not have a 3rd row, but a_{23} is -1.

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 2 rows and 3 columns is said to be of order 2x3. Understanding the order is crucial for performing operations like addition, multiplication, and determining compatibility with other matrices.

Matrix Elements

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

Matrix Notation

Matrix notation involves the use of brackets to enclose the elements of the matrix, which can be organized in rows and columns. This notation helps in visualizing and manipulating matrices in algebraic expressions. Proper notation is important for clarity, especially when discussing specific elements or performing matrix operations.