Example 2.24 (Basis Change) - how to get S

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Describe the mistake
Example 2.24 does describe how to populate S for a general basis B, in last sentence on page 57:
For a general basis B,
we would need to solve a linear equation system to find the λi such that
\sum_{i=1}^3 λibi = ˜bj , j = 1, . . . , 3.

But seems a bit clearer to add the "j" subscript to λi so it would be λij, to match the "j" subscript in bj on rhs of equation.

Location
Please provide the

1. version (bottom of page) Draft (2024-01-15)
2. Chapter: 2
3. page: 58
4. line number/equation number: first line at top of page

Proposed solution
\sum_{i=1}^3 λijbi = ˜bj , j = 1, . . . , 3.

I would also suggest to add explicitly that ^^ is same as trying to solve for S:
B S = ˜B

Additional context
I found very insightful the explanation given on Sep 23 in this issue 776: #776.

In particular:
S transforms coordinate vectors wrt to bases \tilde{B} and B: \hat{x}B = S \hat{x}{\tilde{B}}