Find the Norm
Problem
∥[[5,10,15,20,25,30,35,40,45],[0.6,0.9,1.2,1.4,1.6,1.7,1.9,2.1,2.2]]∥
Solution
Identify the type of norm to be calculated. Since the specific norm is not specified for this 2×9 matrix, the Frobenius norm ∥A∥ is the standard default, calculated as the square root of the sum of the squares of all elements.
Square each element in the first row.
5^2=25
10^2=100
15^2=225
20^2=400
25^2=625
30^2=900
35^2=1225
40^2=1600
45^2=2025
Square each element in the second row.
0.6^2=0.36
0.9^2=0.81
1.2^2=1.44
1.4^2=1.96
1.6^2=2.56
1.7^2=2.89
1.9^2=3.61
2.1^2=4.41
2.2^2=4.84
Sum all the squared values from both rows.
(∑_^)((row_1)^2)=25+100+225+400+625+900+1225+1600+2025=7125
(∑_^)((row_2)^2)=0.36+0.81+1.44+1.96+2.56+2.89+3.61+4.41+4.84=22.88
Total Sum=7125+22.88=7147.88
Take the square root of the total sum to find the Frobenius norm.
∥A∥=√(,7147.88)
∥A∥≈84.54513587
Final Answer
∥[[5,10,15,20,25,30,35,40,45],[0.6,0.9,1.2,1.4,1.6,1.7,1.9,2.1,2.2]]∥=√(,7147.88)≈84.5451
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