matrix A =

1 1

2 2

And vector b =

2

3

Whats the value of (A*b)t * (A*b) ?

Question

matrix A =

1 1

2 2

And vector b =

2

3

Whats the value of (A*b)t * (A*b) ?

BlackTom AI · Accepted Answer

We start by identifying the given matrix and vector, and how to combine them.
A is the 2x2 matrix with rows [1,1] and [2,2]. So A = [[1, 1], [2, 2]].
b is the column vector with entries 2 and 3, so b = [2, 3]^T.
Next, compute the product A*b. Multiply A by b:
- First entry: 1*2 + 1*3 = 2 + 3 = 5
- Second entry: 2*2 + 2*3 = 4 + 6 = 10
Thus A*b = [5, 10]^T.
Now we need (A*b)^t * (A*b), which is the dot product of A*b with itself, i.e., the squared length or squared Euclidean norm of A*b.
Compute the dot product: 5^2 + 10^2 = 25 + 100 = 125.
Therefore, the correct value is 125. The provided answer 121 does not match this calculation, indicating a potential error in the given answer.
Note on the structure: since (A*b)^t*(A*b) = ||A*b||^2, it should always yield a nonnegative scalar equal to the sum of squares of the components of A*b. In this case, that sum is 125, not 121.

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 12. Quiz for Class 12

matrix A = 1 1 2 2 And vector b = 2 3 Whats the value of (Ab)t (A*b) ?

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