Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Please use the technique provided above the question to find the answer. Thank you.
![Determinants of 2 × 2 and 3 × 3 matrices can be evaluated very efficiently using the pattern
suggested below
all
a21
912
822
-
a) A =
In the 2 × 2 case, the determinant can be computed by forming the product of the entries on the
rightward arrow and subtracting the product of the entries on the leftward arrow.
In the 3 x 3 case we first recopy the first and second columns as shown in the figure, after
which we can compute the determinant by summing the products of the entries on the rightward
arrows and subtracting the products on the leftward arrows.
For example
-4
7
3 1
4 -2
258
3
6
9
=
all a12 013 911
922 923 821
a21
631
932
1
= -4
931
= (3)(-2) – (1)(4) = −10
-
C
b) A = 2
L4
b
Warning: This trick does not work for matrices of size 4 x 4 or higher.
= [45+84 +96] - [105-48-72] = 240
912
922
632
5
4. Use the above arrow technique to compute the determinants of the following matrices.
[-2 7 6
5
1 -2
3
8
4
-4
1
C-1
3231](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0e10355-5716-44c5-8858-66d52fccb53f%2F9536b7b4-76c9-4659-96f0-dc8f04ec551c%2Fyavpqky_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determinants of 2 × 2 and 3 × 3 matrices can be evaluated very efficiently using the pattern
suggested below
all
a21
912
822
-
a) A =
In the 2 × 2 case, the determinant can be computed by forming the product of the entries on the
rightward arrow and subtracting the product of the entries on the leftward arrow.
In the 3 x 3 case we first recopy the first and second columns as shown in the figure, after
which we can compute the determinant by summing the products of the entries on the rightward
arrows and subtracting the products on the leftward arrows.
For example
-4
7
3 1
4 -2
258
3
6
9
=
all a12 013 911
922 923 821
a21
631
932
1
= -4
931
= (3)(-2) – (1)(4) = −10
-
C
b) A = 2
L4
b
Warning: This trick does not work for matrices of size 4 x 4 or higher.
= [45+84 +96] - [105-48-72] = 240
912
922
632
5
4. Use the above arrow technique to compute the determinants of the following matrices.
[-2 7 6
5
1 -2
3
8
4
-4
1
C-1
3231
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