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Let A be invertible square matrix such that 4A^2 + 6A = I, where I is identity matrix
A) Prove that 2A^3 - 5A + 0.75I = 0 where 0 is the zero matrix
B) Hence determine the value for C such that CA^-1 = 10I - 4A^2
What I got so far for part A after subbing I into the equation is:
8A^3 + 12A^2 - 2A
I wonder whether I can factorise the matrix as:
= 2A ( 4A^2 + 6A - I)
= 2A (I-I)
= 0
And I have no idea for part B.
Can you please help???
A) Prove that 2A^3 - 5A + 0.75I = 0 where 0 is the zero matrix
B) Hence determine the value for C such that CA^-1 = 10I - 4A^2
What I got so far for part A after subbing I into the equation is:
8A^3 + 12A^2 - 2A
I wonder whether I can factorise the matrix as:
= 2A ( 4A^2 + 6A - I)
= 2A (I-I)
= 0
And I have no idea for part B.
Can you please help???