If A = [[2, −1], [−1, 2]], then A² − 4A + 3I is equal to: A. 0 B. I C. 2I D. 3I Answer: A) 0 Explanation: A² = [[2, −1], [−1, 2]] × [[2, −1], [−1, 2]] = [[4+1, −2−2], [−2−2, 1+4]] = [[5, −4], [−4, 5]]. 4A = [[8, −4], [−4, 8]]. A² − 4A = [[−3, 0], [0, −3]] = −3I. Then A² − 4A + 3I = −3I + 3I = 0.

imo class 12 matrices

If A = [[2, −1], [−1, 2]], then A² − 4A + 3I is equal to:

VAVidaara Admin Asked 6d ago 0 views 0 answers

#IMO #Class 12 #Mathematics #Matrices #mathematical-reasoning

If A = [[2, −1], [−1, 2]], then A² − 4A + 3I is equal to:

A. 0
B. I
C. 2I
D. 3I

Answer: A) 0

Explanation: A² = [[2, −1], [−1, 2]] × [[2, −1], [−1, 2]] = [[4+1, −2−2], [−2−2, 1+4]] = [[5, −4], [−4, 5]]. 4A = [[8, −4], [−4, 8]]. A² − 4A = [[−3, 0], [0, −3]] = −3I. Then A² − 4A + 3I = −3I + 3I = 0.

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