The change - of - coordinate matrix from B={[3−14][20−5][8−27]} to the standard basis in RRn.

The change - of - coordinates matrix from a basis B=b1,b2,...,bn to the standadr matrix in RRn is given as, PB=[b1b2,...,bn] Here, n is the number of vectors in a basis. There are three vectors in the given basis, The given basis is cB={[3−14][20−5][8−27]}. Thus, the change-of-coordinates matrix from B to the standard basis in RR3 is, PB=[b1b2b3] [328−10−24−57] Therefore, the change-of-coordinates matrix is [328−10−24−57]

"The change - of - coordinate matrix from..." was answered by our experts

Emily-Jane Bray

Answered question

2021-02-25

The change - of - coordinate matrix from

B = {[\begin{matrix} 3 \\ - 1 \\ 4 \end{matrix}] [\begin{matrix} 2 \\ 0 \\ - 5 \end{matrix}] [\begin{matrix} 8 \\ - 2 \\ 7 \end{matrix}]}

to the standard basis in

R R^{n} .

Answer & Explanation

au4gsf

Skilled2021-02-26Added 95 answers

The change - of - coordinates matrix from a basis

B = b_{1}, b_{2}, . . ., b_{n}

to the standadr matrix in

R R^{n}

is given as,

P_{B} = [b_{1} b_{2}, . . ., b_{n}]

Here, n is the number of vectors in a basis.
There are three vectors in the given basis,
The given basis is c

B = {[\begin{matrix} 3 \\ - 1 \\ 4 \end{matrix}] [\begin{matrix} 2 \\ 0 \\ - 5 \end{matrix}] [\begin{matrix} 8 \\ - 2 \\ 7 \end{matrix}]}

.
Thus, the change-of-coordinates matrix from

B

to the standard basis in

R R^{3}

is,

P_{B} = [b_{1} b_{2} b_{3}]

[\begin{matrix} 3 & 2 & 8 \\ - 1 & 0 & - 2 \\ 4 & - 5 & 7 \end{matrix}]

Therefore, the change-of-coordinates matrix is

[\begin{matrix} 3 & 2 & 8 \\ - 1 & 0 & - 2 \\ 4 & - 5 & 7 \end{matrix}]

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Didn't find what you were looking for?