Find the Norm [[2,1],[-3,-1]]

Problem

‖[2,1],[−3,−1]‖

Solution

1. Identify the type of norm to be calculated. Since no specific norm was requested (e.g., (L_1) (L_∞), the Frobenius norm is the standard default for a matrix, which is the square root of the sum of the squares of all elements.

2. Square each individual element of the matrix.

2=4

1=1

(−3)2=9

(−1)2=1

3. Sum the squared values together.

4+1+9+1=15

4. Take the square root of the resulting sum to find the Frobenius norm.

√(,15)

Final Answer

‖[2,1],[−3,−1]‖F=√(,15)

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