FC8 - Week 3-1-16

📌 Essential for understanding systems of equations and transformations in higher dimensions.

🔹 What is a Triangular Matrix?

🔹 Answer: A triangular matrix is a matrix where all the elements above or below the main diagonal are zero. There are two types:

• Upper Triangular Matrix: All elements below the main diagonal are zero.

• Lower Triangular Matrix: All elements above the main diagonal are zero.

🔹 What is Gaussian Elimination?

🔹 Answer: Gaussian elimination is a method for solving a system of linear equations by using elementary row operations to transform the coefficient matrix into an upper triangular form, then solving for the unknowns from last to first.

🔹 What is the Determinant of a Matrix?

🔹 Answer: The determinant is a numerical value assigned to a square matrix, indicating important properties such as invertibility. If the determinant is zero, the matrix is singular and does not have an inverse.

🔹 What is the Role of the Coordinate System in Linear Algebra?

🔹 Answer: The coordinate system is used in linear algebra to represent vectors in 2D and 3D space. Each vector can be represented as a point or direction in the coordinate plane.

🔹 What is a Pivot in a Matrix?

🔹 Answer: A pivot is an element in a matrix that serves as the basis for elementary row operations in Gaussian elimination. It is usually the first nonzero number in a row.

🔹 How is Matrix Multiplication Performed?

🔹 Answer: To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second. The element (i,j) in the resulting matrix is obtained by summing the products of corresponding elements in row iii of the first matrix and column j of the second.