if a is a square matrix such that a² = a, then write the value of 7a - (i + a)³ where i is an identity matrix.
Answers
Answered by
2
Answer:
given A2=A
7A−(I+A)3=7A−[I3+3A2I+3AI2+A3]
=7A−[I+3A+3A+A2.A]
=7A−[I+3A+3A+A]
=7A−I+7A
=−I
Answered by
1
Answer:
-i
Step-by-step explanation:
Given: a² = a
7a - (i + a)³
⇒ 7a - (i³ + a³ + 3 * i² * a + 3 * a * i²)
⇒ 7a - (i + a³ + 3a + 3a²)
⇒ 7a - (i + a * a² + 3a + 3a²)
⇒ 7a - (i + a * a + 3a + 3a) [∵ a² = a]
⇒ 7a - (i + a² + 6a)
⇒ 7a - (i + a + 6a)
⇒ 7a - (i + 7a)
⇒ 7a - i - 7a
⇒ -i
Therefore,
7a - (i + a)³ = -i
Hope it helps!
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