Mark each statement True or False, and justify your answer. a. If A is an n×n matrix such that A² = I, then A is invertible. b. The set W of all nxn matrices A whose trace is equal to 1 is a subspace of M nxn [The trace tr A of the nxn matrix A=(a;;) is defined as the sum of the entries on its main diagonal: tr A = a₁ + a₂2+...+amm ·] 11 nn

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Mark each statement True or False, and justify your answer.
a. If A is an n×n matrix such that A² = I, then A is invertible.
b. The set W of all n×n matrices A whose trace is equal to 1 is a subspace of M,
nxn
[The trace tr A of the nxn matrix A=(a;;) is defined as the sum of the entries on
n×n
its main diagonal:
tr A = a₁₁ +a₂2+...+amn •]
nn
Transcribed Image Text:Mark each statement True or False, and justify your answer. a. If A is an n×n matrix such that A² = I, then A is invertible. b. The set W of all n×n matrices A whose trace is equal to 1 is a subspace of M, nxn [The trace tr A of the nxn matrix A=(a;;) is defined as the sum of the entries on n×n its main diagonal: tr A = a₁₁ +a₂2+...+amn •] nn
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