2.4. Consider an n × n nonsingular matrix A11 A12 A = where A₁1 is m × m (m < n). Assume that A22 and A11 := A11 A12A22

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2 4 Consider An N N Nonsingular Matrix A11 A12 A Where A 1 Is M M M N Assume That A22 And A11 A11 A12a22 1 (141.01 KiB) Viewed 38 times

2.4. Consider an n × n nonsingular matrix A11 A12 A = where A₁1 is m × m (m < n). Assume that A22 and A11 := A11 A12A22 A21 are nonsingular. (a) Show that A-¹ is given by ù -Ã₁¹A12A22² -1 –A₂²¹²А²₁Ãμ¹¹² №₂₂²¹ + A₂²¹A₂1Ã₁¹²¹A12A22² Exercises 61 (b) Show that det(A) = det(A22) · det(A11 – A12A22¹ A21). (c) Use (a) and (b) to derive the conditional distribution of Y₁ given Y2 = y2 in Section 2.3.2.