Find the Norm [[1,2,-9,-8],[0,1,7,-3],[0,0,1,7]]

Problem

‖[1,2,−9,−8],[0,1,7,−3],[0,0,1,7]‖

Solution

1. Identify the type of norm to be calculated. Since no specific norm was requested (such as the (L_1) or (L_∞) norm), the standard Frobenius norm ∥A∥ is typically used for matrices, which is the square root of the sum of the squares of all elements.

2. Square each individual element of the matrix.

1^2=1

2^2=4

(−9)^2=81

(−8)^2=64

0^2=0

1^2=1

7^2=49

(−3)^2=9

0^2=0

0^2=0

1^2=1

7^2=49

3. Sum all the squared values together.

1+4+81+64+0+1+49+9+0+0+1+49=259

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

√(,259)

Final Answer

‖[1,2,−9,−8],[0,1,7,−3],[0,0,1,7]‖_F=√(,259)

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