4. Find the condition of c in terms of c and c3 such that the following...

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4. Find the condition of c₁ in terms of c₂ and c3 such that the following linear system is solvable: 1 -1 (30-0) 4 -2 2 1 = 5. Let I be a 2 x 2 identity matrix. Define A= (1-3) (a) By induction, prove that A" = 3¹A +33"I for all n e Zt. (b) Does A" converge when n→ ∞0? 4. Find the condition of c₁ in terms of c₂ and c3 such that the following linear system is solvable: 1 -1 (30-0) 4 -2 2 1 = 5. Let I be a 2 x 2 identity matrix. Define A= (1-3) (a) By induction, prove that A" = 3¹A +33"I for all n e Zt. (b) Does A" converge when n→ ∞0?