Suppose ·1,·2 are two norms on ℝ^n. Prove that the corresponding matrix norms satisfy c^⋆A1 ≤A2

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Step 1: **Understand the definitions of matrix norms induced by vector norms.**u000AThe matrix norm

Suppose $\|\cdot\|_1,\|\cdot\|_2$ are two norms on $\mathbb{R}^n$. Prove that the corresponding matrix norms satisfy $\widehat{c}^{\star}\|A\|_1 \leq\|A\|_2 \leq \hat{C}^{\star}\|A\|_1$ for any $n \times n$ matrix $A$ for some positive constants $0<\widehat{c}^{\star}<\hat{C}^{\star}$.