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Text: Problems 10 can be solved using properties of determinants. Given that det |A| = d, compute the determinant of the matrix: [A] = | 1 2 3 | | 4 5 6 | | 7 8 9 | in terms of d. Explain. Given matrix equation: AB - C. det(A) = 20, det(C) - 10. Evaluate det(B).

Text: Problems 10 can be solved using properties of determinants. Given that det |A| = d, compute the determinant of the matrix: [A] = | 1 2 3 | | 4 5 6 | | 7 8 9 | in terms of d. Explain. Given matrix equation: AB - C. det(A) = 20, det(C) - 10. Evaluate det(B).

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Discover Prove: Determinant Formula for the Area of a Triangle The figure shows a triangle in the plane with vertices (a1, b1),(a2, b2), and (a3, b3). (a) Find the coordinates of the vertices of the surrounding rectangle, and find its area. (b) Find the area of the red triangle by subtracting the areas of the three blue triangles from the area of the rectangle. (c) Use your answer to part (b) to show that the area S A of the red triangle is given by A= ±(1)/(2)| a1 b1 1 a2 b2

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