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Determinants and Vector Expressions: Practicing Linear Algebra Concepts

This resource provides a series of exercises focused on determinants and vector calculations. Students are tasked with finding the value of various determinants similar to specified problems, as well as calculating cross products of vectors. Additionally, the exercises involve using given vectors to find specific expressions and explore orthogonal vectors. The content emphasizes understanding linear algebra concepts, with examples that help reinforce the theoretical material presented in textbooks.

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Determinants and Vector Expressions: Practicing Linear Algebra Concepts

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  1. The Cross Product

  2. 1. Find the value of each determinant(Similar to p.370 #7-10)

  3. 2. Find the value of each determinant(Similar to p.370 #11-14)

  4. 3. Find (a) v x w, (b) w x v, (c) w x w, and (d) v x v(Similar to p.370 #15-22)

  5. 4. Find (a) v x w, (b) w x v, (c) w x w, and (d) v x v(Similar to p.370 #15-22)

  6. 5. Use the given vectors u, v, and w to find each expression.u = 3i – j + 2kv = 4i + j – 5kw = i + j + k(Similar to p.370 #23-40)

  7. 6. Use the given vectors u, v, and w to find each expression.u = 3i – j + 2kv = 4i + j – 5kw = i + j + k(Similar to p.370 #23-40)

  8. 7. Use the given vectors u, v, and w to find each expression.u = 3i – j + 2kv = 4i + j – 5kw = i + j + k(Similar to p.370 #23-40)

  9. 8. Use the given vectors u, v, and w to find each expression.u = 3i – j + 2kv = 4i + j – 5kw = i + j + k(Similar to p.370 #23-40)

  10. 9. Use the given vectors u, v, and w to find each expression.u = 3i – j + 2kv = 4i + j – 5kw = i + j + k(Similar to p.370 #41-44)vector orthogonal to both u and v (Hint u x v is orthogonal to both)

  11. 11. Find the area of the parallelogram with vertices P1, P2, P3, and P4(Similar to p.370 #49-52)

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