Let y = (2 6) and u = (7 1). Write y as the sum of a vector in Span(u) and a vector orthogonal to .

The question is missing. Here is the complete question.

Let y = and u = . Write y as the sum of a vector in Span(u) and a vector orthogonal to u.

y =

Step-by-step explanation: The sum of vectors is given by

y =   + z

where   is in Span(u);

vector z is orthogonal to it;

First you have to compute the orthogonal projection of y:

= proj y =

Calculating orthogonal projection:

. =

. =

Calculating vector z:

z = y -

z =

z =

Writing y as the sum:

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