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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.$$\left|\begin{array}{lll}{1} & {3} & {4} \\ {2} & {3} & {1} \\ {3} & {3} & {2}\end{array}\right|$$

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Algebra

Chapter 3

Determinants

Section 1

Introduction to Determinants

Introduction to Matrices

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okay. In this example, we want to find the determines off this matrix using this trick right here. So the first thing we have to copy the 1st 2 rows First columns onto the right side. So have 123 33 and three. The multiplying the diagonals. And these diagonals we get one times three times to, which is six plus three times one time, three get in line. Plus four times. Two times three, which is eight times three, which is six times 4 24 minus three times, three times, for which is nine times for which should give you 36. Why does three times? One times one, which is three minus two times two times three, which is 12. So this is equal to 39 minus by 36 months. Three is 39 minus 12. So this is my soul.

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