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

1. 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.

2. Square each element in the first row.

5=25

10=100

15=225

20=400

25=625

30=900

35=1225

40=1600

45=2025

3. Square each element in the second row.

0.6=0.36

0.9=0.81

1.2=1.44

1.4=1.96

1.6=2.56

1.7=2.89

1.9=3.61

2.1=4.41

2.2=4.84

4. 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

5. 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

Want more problems? Check here!