Find the Norm [[3,-3,-6,-3],[2,-2,-4,h],[-2,3,-4,7]]

Problem

‖[3,−3,−6,−3],[2,−2,−4,h],[−2,3,−4,7]‖F

Solution

1. Identify the type of norm to be calculated. For a matrix, the default norm is typically the Frobenius norm, which is the square root of the sum of the squares of all elements.

2. Square each individual element in the matrix.

3=9

(−3)2=9

(−6)2=36

(−3)2=9

2=4

(−2)2=4

(−4)2=16

h2=h2

(−2)2=4

3=9

(−4)2=16

7=49

3. Sum all the squared values together.

9+9+36+9+4+4+16+h2+4+9+16+49

4. Simplify the sum of the constant terms.

165+h2

5. Apply the square root to the sum to find the Frobenius norm.

√(,165+h2)

Final Answer

‖[3,−3,−6,−3],[2,−2,−4,h],[−2,3,−4,7]‖F=√(,h2+165)

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