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muthuraman
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A is invertible... How give me the proper explanation...
I presume you meant determinant is NOT zero.HallsofIvy said:A matrix is invertible if and only if its determinant is 0. And for any triangular matrix, the determinant is simply the product of the numbers on the diagonal.
Yes, of course. Thank you!mathman said:I presume you meant determinant is NOT zero.
A triangular matrix is a special type of square matrix where all the entries above or below the main diagonal are zero. This means that the entries either form an upper triangular matrix (all entries below the main diagonal are zero) or a lower triangular matrix (all entries above the main diagonal are zero).
To determine if a matrix is triangular, you can check if all the entries above or below the main diagonal are zero. If this condition is met, the matrix is triangular. Additionally, you can also check if the matrix is either an upper or lower triangular matrix by looking at the position of the non-zero entries.
The main diagonal of a matrix refers to the set of entries that are located from the top left corner to the bottom right corner of the matrix. These are the entries where the row and column indices are equal, and they divide the matrix into two equal parts.
No, a triangular matrix cannot have zero entries on the main diagonal. This is because the main diagonal is defined as the set of entries where the row and column indices are equal, and for a triangular matrix, all entries on the main diagonal must be non-zero.
Triangular matrices are commonly used in mathematical and scientific computations, particularly in solving systems of linear equations. They are also used in data analysis, signal processing, and computer graphics. Additionally, triangular matrices have applications in engineering, economics, and physics.