Find the Norm [[1,-4,10],[0,0,0]]

Problem

‖[1,−4,10],[0,0,0]‖

Solution

1. Identify the type of norm to be calculated. Since no specific norm was requested, the standard Frobenius norm (the Euclidean norm for matrices) is typically used.

2. Square each individual element of the matrix.

1=1

(−4)2=16

10=100

0=0

3. Sum all the squared values together.

1+16+100+0+0+0=117

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

√(,117)

5. Simplify the radical by factoring out perfect squares.

√(,9⋅13)=3√(,13)

Final Answer

‖[1,−4,10],[0,0,0]‖F=3√(,13)

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