1.2. Types of Matrices

Types of Matrices Based on Triangular Structure

1. Upper Triangular Matrix

A square matrix where all elements below the leading diagonal are zero.
Example:

Upper Triangular Matrix

\[\Large Upper\;Triangular\;Matrix\;C = \begin{bmatrix} \color{red}{2} & 4 & 6 \\ \color{blue}{0} & \color{red}{5} & 9 \\ \color{blue}{0} & \color{blue}{0} & \color{red}{3} \end{bmatrix} \]

2. Lower Triangular Matrix

A square matrix where all elements above the leading diagonal are zero.
Example:

Lower Triangular Matrix

\[\Large Lower\;Triangular\;Matrix\;C = \begin{bmatrix} \color{red}{2} & \color{blue}{0} & \color{blue}{0} \\ 4 & \color{red}{5} & \color{blue}{0} \\ 6 & 9 & \color{red}{3} \end{bmatrix} \]

MCQ – Types of Matrices

Which of the following is true about an Upper and Lower Triangular Matrix?

All elements below the main diagonal in an Upper Triangular Matrix are zero, and in a Lower Triangular Matrix, elements above the main diagonal are zero. All elements above the main diagonal in an Upper Triangular Matrix are zero, and in a Lower Triangular Matrix, elements below the main diagonal are zero. An Upper Triangular Matrix has non-zero elements only on the main diagonal, and a Lower Triangular Matrix has non-zero elements above the diagonal. Both Upper and Lower Triangular Matrices are square matrices where all elements are zero except the diagonal.

UNITRICS

Types of Matrices Based on Triangular Structure

1. Upper Triangular Matrix

2. Lower Triangular Matrix

UNITRICS

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