MAT2114 Homework §4.2 Name: Due Date: 01 April 2022 Honor Code: I neither gave nor received unauthorized help on this assignment. Instructions: Answer the following questions, showing ALL your work...

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MAT2114 Homework §4.2 Name: Due Date: 01 April 2022 Honor Code: I neither gave nor received unauthorized help on this assignment. Instructions: Answer the following questions, showing ALL your work and writing neatly. This assignment is due to Canvas by 11:59pm on the date above. Group work is allowed and encouraged, but each group member must write up their own solutions. 1. Recall that a block-diagonal matrix is a square matrix of the form B1 B2 . . . Bk  where each of the Bi’s are square matrices (possibly of different sizes) and all blank spaces are zeroes. A block diagonal is about as close to being diagonal as one can hope. The matrix in §4.2 WebAssign, Problem #5 is block-diagonal with two 2 × 2 blocks, call them B1 and B2. (a) Compute det(B1). (b) Compute det(B2). (c) What do you notice about the determinant you computed in that WebAssign problem? 1 MAT2114 Homework §4.2 2. Any invertible n× n matrix A has the property that A−1 = 1 det(A) B for some n× n matrix B. We’ve already seen this in the case of 2 × 2’s: If A = [ a b c d ] , then A−1 = 1 det(A) B where B = [ d −b −c a ] . Find the matrix B in the 3 × 3 case: If A = a b cd e f g h j  , then A−1 = 1 det(A) B where B = � � �� � � � � �  . (As you can see, it is not worth memorizing the formula for the inverse of a 3 × 3 and Gauss–Jordan is almost certainly a much better method.) 2 Hw 4.1