Find the Norm [[x,2,3,4,5,6],[y,-1,1,3,5,7]]

Problem

[[2,3,4,5,6],[−1,1,3,5,7]]

Solution

1. Identify the task as finding the Frobenius norm of the given matrix A which is the square root of the sum of the squares of all its elements.

2. Square each element in the first row: 2^2=4 3^2=9 4^2=16 5^2=25 and 6^2=36

3. Square each element in the second row: (−1)^2=1 1^2=1 3^2=9 5^2=25 and 7^2=49

4. Sum all the squared values: $4 + 9 + 16 + 25 + 36 + 1 + 1 + 9 + 25 + 49 = 175$.

5. Take the square root of the sum to find the norm: √(,175)

6. Simplify the radical expression: √(,25⋅7)=5√(,7)

Final Answer

∥[[2,3,4,5,6],[−1,1,3,5,7]]∥=5√(,7)

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