Find the Norm [[1,0],[6,-1]]

Problem

‖[1,0],[6,−1]‖

Solution

1. Identify the matrix A as a 2×2 matrix where A=[[1,0],[6,−1]] Since the specific type of norm is not specified, the Frobenius norm is the standard default for general matrices.

2. Apply the formula for the Frobenius norm, which is the square root of the sum of the squares of all elements in the matrix.

∥A∥=√(,(∑_i,j^)(|)*(a_i,j)|2)

3. Substitute the values from the matrix into the formula.

∥A∥=√(,1+0+6+(−1)2)

4. Simplify the expression inside the square root by calculating the squares.

∥A∥=√(,1+0+36+1)

5. Calculate the final sum and simplify the radical.

∥A∥=√(,38)

Final Answer

‖[1,0],[6,−1]‖F=√(,38)

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