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The expansion of a $3 \times 3$ determinant can be remembered by the following device. Write a second copy of the first two columns to the right of the matrix, and compute the determinant by multiplying entries on six diagonals:Graph cannot copyAdd the downward diagonal products and subtract the upward products. Use this method to compute the determinants in Exercises $15-18 .$ Warning: This trick does not generalize in any reasonable way to $4 \times 4$ or larger matrices.$$\left|\begin{array}{rrr}{0} & {3} & {1} \\ {4} & {-5} & {0} \\ {3} & {4} & {1}\end{array}\right|$$

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Algebra

Chapter 3

Determinants

Section 1

Introduction to Determinants

Introduction to Matrices

Oregon State University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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in this example. We want to find the determines all the three by three matrix using this strip right here. So the first step to perform industry is we have to copy the 1st 2 columns. Yeah, to copy them over. We have zero for three, 35 and four. Then we'll multiply down on these, diagnose and multiply up on these. So is there times five times? One gives you zero plus three times during times free, which gives you the right plus one times four times for which gives you 16 and who, minus by three times five times of one, which is 50 minus by four times. There are times right, which is doing minus by one times four times street, which should give you 12. This is 16 minus 15 miles to which is one months, 12 and six equal to my system.

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