5. Given the points A = (0,0), B = (5,1), C = (2,6) on the plane....
6. Given the points A = (0,0),B = (5,1),C = (2,6) on the plane. Use a determinant to find the area of the triangle ABC.
6. Given the points A = (0,0), B = (5,1), C = (2,6) on the plane. Use a determinant to find the area of the triangle ABC. 7. Let T:V - W be a linear transformation, and let V1, V2, ..., Un be vectors in V. Suppose that T(vi), T(02),...,T(un) are linearly independent. Show that V1, V2, ..., Vn are linearly independent.
6. Given the points A = (0,0), B = (5,1), C = (2,6) on the plane. Use a determinant to find the area of the triangle ABC. 7. Let T:V - W be a linear transformation, and let V1, V2, ..., Un be vectors in V. Suppose that T(vi), T(02),...,T(un) are linearly independent. Show that V1, V2, ..., Vn are linearly independent.
6 and 7!!! 6. Given the points A - (0,0), B = (5,1),C - (2,6) on the plane. Use a determinant to find the area of the triangle ABC. 7. Let T:V - W be a linear transformation, and let 01,03,...,U, be vectors in V. Suppose that T(u), 7(v2),...,T(v.) are linearly independent. Show that 01,03,.., are linearly independent
6. Given the points A = (0,0), B = (5,1), C = (2,6) on the plane. Use a determinant to find the area of the triangle ABC. 7. Let T:V - W be a linear transformation, and let V1, V2, ..., Un be vectors in V. Suppose that T(vi), T(02),...,T(un) are linearly independent. Show that V1, V2, ..., Vn are linearly independent. 3. Given that 8 - ...) is a basis for a vector space V. Determine if 3 -...
SOLVE BOTH 6 and 7 6. Given the points A - (0,0), B = (5,1), (2,6) on the plane. Use a determinant to find the area of the triangle ABC. 7. Let T:V - W be a linear transformation, and let 01, 02, ..., Urbe vectors in V. Suppose that T(u), 7(2),...,T(un) are linearly independent. Show that 01, 02,..., Un are linearly independent.
2. (5 points) (a) Find a vector perpendicular to the plane through the points A(0, -2,0), B(4,1, -2) and C(5,3,1). (b) Find an equation of the plane through the points A, B, and C. (b) Find the area of the triangle ABC.
2. (5 points) (a) Find a vector perpendicular to the plane through the points A(0, -2,0), B(4,1, -2) and C(5,3,1). (b) Find an equation of the plane through the points A, B, and C. (b) Find the area of the triangle ABC.
9.) (12 pts.) Let loop C be the triangle with vertices (0,0), (2,0), and (2,6). Evaluate the line integral $ ay dx + (x - y) dy using one of Green's Theorems.
Let A = (2,7), B = (-1,4) and C = (3,0) be points on the plane Let l be the line whose equation is x+ky=0 for some real number k. Find all values of k so that l meet the triangle ABC.