Subjects linear algebra

Second Diagonal F8285A

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. The problem asks: What is the second diagonal? 2. In a square or rectangular matrix, the "second diagonal" usually refers to the secondary diagonal, also called the anti-diagonal or minor diagonal. 3. The primary diagonal runs from the top-left corner to the bottom-right corner. The secondary diagonal runs from the top-right corner to the bottom-left corner. 4. For an $n \times n$ matrix $A = [a_{ij}]$, the elements on the secondary diagonal satisfy the condition $i + j = n + 1$. 5. For example, in a $3 \times 3$ matrix, the secondary diagonal elements are $a_{13}$, $a_{22}$, and $a_{31}$. 6. To find the secondary diagonal elements, you select elements where the row index plus the column index equals $n + 1$. 7. This is important in many matrix operations, such as calculating the trace of the secondary diagonal or checking symmetry properties. Final answer: The second diagonal (secondary diagonal) of an $n \times n$ matrix consists of elements $a_{ij}$ where $i + j = n + 1$.