Find the Norm -3A=[[-9,-1],[-2,-3]]

Problem

∥−3*A∥ where −3*A=[[−9,−1],[−2,−3]]

Solution

1. Identify the matrix for which the norm is being calculated. The matrix is M=[[−9,−1],[−2,−3]]

2. Determine the type of norm to be calculated. In the absence of a specific subscript (like 1 2 or ∞, the Frobenius norm (also known as the Euclidean norm for matrices) is typically used.

3. Apply the formula for the Frobenius norm, which is the square root of the sum of the squares of all elements in the matrix.

∥M∥=√(,(∑_i,j^)(|)*(a_i,j)|2)

4. Substitute the values from the matrix into the formula.

∥−3*A∥=√(,(−9)2+(−1)2+(−2)2+(−3)2)

5. Calculate the squares of the individual elements.

∥−3*A∥=√(,81+1+4+9)

6. Sum the squared values.

∥−3*A∥=√(,95)

Final Answer

∥−3*A∥=√(,95)

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