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?
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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
c d
]
, then A−1 =
1
det(A)
B where B =
[
d −
−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.)
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Hw 4.1