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LAHW#08

LAHW#08. Due ∞. 4.1 Determinants: Introduction. 2. Let For what values of the parameter β will the system have a unique solution?. 4.1 Determinants: Introduction. 8. Use the determinantal criterion for noninvertibility (singularity) to find all the values of t for which the

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LAHW#08

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  1. LAHW#08 Due ∞

  2. 4.1 Determinants: Introduction • 2. • LetFor what values of the parameter β will the system have a unique solution?

  3. 4.1 Determinants: Introduction • 8. • Use the determinantal criterion for noninvertibility (singularity) to find all the values of t for which the matrix is noninvertible (singular).

  4. 4.1 Determinants: Introduction • 11. • Let A = Using Properties I, II, and III and Theorem 1, calculate the determinant of A.

  5. 4.1 Determinants: Introduction • 12. • Let A = . Compute the determinant of A by using the row replacement operation only (no scaling or swapping).

  6. 4.1 Determinants: Introduction • 31. • Let u = (u1, u2), v = (v1, v2), p = (u1, v1) and q = (u2, v2). Do the triangles △(0,u,v) and △(0,p,q) have the same area? (Verify or give a counterexample.) Draw the triangles involved here in a concrete case, such as u = (5, 1) and v = (4, 3), and compute the two areas in question.

  7. 4.1 Determinants: Introduction • 34. • Explain why a 2 × 2 matrix A has this property: Det(αA) = α2Det(A) for α, a scalar. Then prove the corresponding result for n × n matrices.

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