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Show that if A is a square matrix that satisfies the equation 2 A²-A-I-O, then its inverse is A-¹ = 2 A-I. The equation 24² - A - I = O implies that ---Select--- It follows that ---Select-- v Notice the last equation means that ---Select--- multiplied with A is the identity, which is what we wanted to prove.

Show that if A is a square matrix that satisfies the equation 2 A²-A-I-O, then its inverse is A-¹ = 2 A-I. The equation 24² - A - I = O implies that ---Select--- It follows that ---Select-- v Notice the last equation means that ---Select--- multiplied with A is the identity, which is what we wanted to prove.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please fill the --Select-- spaces with the right answer .

The equation 24² - A - I = O implies that ---Select--- Submit Answer . It follows that ---Select--- --Select--- 1=A(1-2A) (21-A)² = -2A +31 = 0 |(21-A)² = A²-4A + 41 I=A |1=2A-A² = (21-A)(21-A) 1=(2A-1) A < 21-A 2A-1 A² - 4A + 41 (21+ A)² -2A + 31 (21-A)² ---Select--- (A-1)(A-1)=0 1=2A-A² 1 = 2A²-A |(21-A)² = A²-4A+41 = A . Notice the last equation means that --Select--- multiplied with A is the identity, which is what we wanted to prove. --Select--- (Ctrl)
Transcribed Image Text:The equation 24² - A - I = O implies that ---Select--- Submit Answer . It follows that ---Select--- --Select--- 1=A(1-2A) (21-A)² = -2A +31 = 0 |(21-A)² = A²-4A + 41 I=A |1=2A-A² = (21-A)(21-A) 1=(2A-1) A < 21-A 2A-1 A² - 4A + 41 (21+ A)² -2A + 31 (21-A)² ---Select--- (A-1)(A-1)=0 1=2A-A² 1 = 2A²-A |(21-A)² = A²-4A+41 = A . Notice the last equation means that --Select--- multiplied with A is the identity, which is what we wanted to prove. --Select--- (Ctrl)
Show that if A is square matrix that satisfies the equation 2 A² - A - I = O, then its inverse is A-¹ = 2 A-I. The equation 24² - A - I = O implies that ---Select--- ✓. It follows that ---Select--- ✓. Notice the last equation means that ---Select--- multiplied with A is the identity, which is what we wanted to prove.
Transcribed Image Text:Show that if A is square matrix that satisfies the equation 2 A² - A - I = O, then its inverse is A-¹ = 2 A-I. The equation 24² - A - I = O implies that ---Select--- ✓. It follows that ---Select--- ✓. Notice the last equation means that ---Select--- multiplied with A is the identity, which is what we wanted to prove.
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