1. Consider a 2 × 2 matrix A = [aij], where aij = \(\frac{(i + j)^2

1.	1. Consider a 2 × 2 matrix A = [aij], where aij = \(\frac{(i + j)^2}{2}\)2. Write the transpose of A. 3. Show that A is symmetric.
Answer» 1. A = \(\begin{bmatrix}2 & \frac{9}{8} \\\frac{9}{2} & 8 \\\end{bmatrix}\) 2. A^T = \(\begin{bmatrix}2 & \frac{9}{8} \\\frac{9}{2} & 8 \\\end{bmatrix}\) 3. A^T = A therefore symmetric matrix.

1. Consider a 2 × 2 matrix A = [aij], where aij = \(\frac{(i + j)^2}{2}\)2. Write the transpose of A. 3. Show that A is symmetric.

Answer»

1. A = \(\begin{bmatrix}2 & \frac{9}{8} \\\frac{9}{2} & 8 \\\end{bmatrix}\)

2. A^T = \(\begin{bmatrix}2 & \frac{9}{8} \\\frac{9}{2} & 8 \\\end{bmatrix}\)

3. A^T = A therefore symmetric matrix.

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