What Does Triangularizing a Matrix Mean in Linear Algebra?

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Triangularizing a matrix involves transforming it into an upper triangular form, where all elements below the main diagonal are zeros. This is achieved through specific row operations, including swapping rows and adding or subtracting multiples of rows. The determinant of the resulting upper triangular matrix can be easily calculated as the product of the diagonal elements. It is important not to multiply or divide any row by a number during this process, as it alters the determinant's value. This method provides a straightforward verification of the determinant calculated using the traditional formula.
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what does triangularizing a matrix mean?
i am supposed to find determinant of a 3 by 3 matrix using big formula, but then I am asked to verify my result by "triangularizing the matrix"
thanks!
 
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Use row operations to reduce the matrix to "upper triangular". That is, a matrix that has only 0's below the main diagonal. You do not need (nor want) to get 1 on the diagonal. If you reduce a matrix to upper triangular using only the row operations of "swap two rows" and "add (or subtract) a multiple of one row to (from) another", and not "multiply (or divide) one row by a number", then the determinant is just the product of the numbers on the main diagonal.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

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