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1516Levered Book Approximation 1Use a second-order Taylor approximation around 0 to estimate (1+2x) (3/2) * (1+-1x) (-1) at x=1/20.数学简单数值题未尝试免费1517Convex Funding Approximation 2Use a second-order Taylor approximation around 0 to estimate (1+1x) (1/2) * (1+3x) (-1) at x=1/50.数学中等数值题未尝试免费1526Determinant After a Rank-One Overlay 1An invertible matrix A has det(A) = 12. For vectors u and v, suppose v T A (-1) u = 1/2. What is det(A + u v T)?数学简单数值题未尝试免费1527Stress-Adjusted Determinant 2An invertible matrix A has det(A) = 5. For vectors u and v, suppose v T A (-1) u = -3/5. What is det(A + u v T)?数学简单数值题未尝试免费1531Residual-Space Projection Rank 1P is a projection on R 8 with rank 3. What is rank(I - P)?数学简单数值题未尝试免费1541Sherman-Morrison Vector Update A 1Suppose A is invertible, A (-1)b = [3, -1] T, A (-1)u = [1, 2] T, v T A (-1)b = 2, and v T A (-1)u = 1/2. What is (A + u v T) (-1) b?数学简单数值题未尝试免费1542Sherman-Morrison Vector Update B 2Suppose A is invertible, A (-1)b = [2, 4] T, A (-1)u = [1, -1] T, v T A (-1)b = -3, and v T A (-1)u = 1/4. What is (A + u v T) (-1) b?数学中等数值题未尝试免费1543Sherman-Morrison Vector Update C 3Suppose A is invertible, A (-1)b = [5, 0] T, A (-1)u = [2, 1] T, v T A (-1)b = 1, and v T A (-1)u = -1/2. What is (A + u v T) (-1) b?数学中等essay未尝试免费1544Sherman-Morrison Vector Update D 4Suppose A is invertible, A (-1)b = [1, 3] T, A (-1)u = [0, 2] T, v T A (-1)b = 4, and v T A (-1)u = 2/3. What is (A + u v T) (-1) b?数学困难数值题未尝试面试订阅1545Sherman-Morrison Failure TestWhy does the Sherman-Morrison formula break down exactly when 1 + v T A (-1)u = 0?数学困难数值题未尝试面试订阅1546Equal-Factor Determinant 1What is det(3 I + 2 11 T) as an n=4 dimensional matrix?数学简单数值题未尝试免费1547Broadcast Matrix Determinant 2What is det(5 I + -1 11 T) as an n=3 dimensional matrix?数学简单数值题未尝试免费1549Ridge-Plus-Ones Determinant 4What is det(4 I + 1/2 11 T) as an n=5 dimensional matrix?数学中等数值题未尝试免费1552Centered Overlay Spectrum 2A = 3I + -111 T in dimension n=5. What are its eigenvalues?数学简单数值题未尝试免费1553Shared-Factor Spectrum 3A = 1I + 211 T in dimension n=3. What are its eigenvalues?数学中等数值题未尝试免费1557Two-Mode Propagation 2A diagonalizable matrix satisfies Au 1 = 4u 1 and Au 2 = 1u 2. If v = 2u 1 + 3u 2, what is A 4v?数学中等derivation未尝试免费1558Diagonalizable Shock Propagation 3A diagonalizable matrix satisfies Au 1 = 3u 1 and Au 2 = 6u 2. If v = -1u 1 + 2u 2, what is A 2v?数学中等数值题未尝试免费1566Trace-and-Square Inference 1A 2x2 matrix has eigenvalues 4 and lambda. Its trace is 10. What is lambda?数学简单数值题未尝试免费1592Recover a Missing Entry from a Cholesky Margin 2A matrix A = [[4, 2], [2, t]] has a Cholesky factor with positive diagonal entries 2 and 3. What is t?数学中等derivation未尝试免费1602Equal-Weight Two-Asset Variance 1Two assets have variances 4 and 9, with covariance 2. What is the variance of the portfolio with weights (1/2, 1/2)?数学简单数值题未尝试免费