Question

Let B = \{b_1, b_2\} and C = \{c_1, c_2\} be bases for $\mathbb{R}^2$. Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B. $\begin{bmatrix} -5\\2 \end{bmatrix}$, $b_2 = \begin{bmatrix} 3\\-1 \end{bmatrix}$, $c_1 = \begin{bmatrix} 1\\2 \end{bmatrix}$, $c_2 = \begin{bmatrix} 1\\1 \end{bmatrix}$ Find the change-of-coordinates matrix from B to C $P_{C \leftarrow B} = \begin{bmatrix} \Box & \Box\\\Box & \Box \end{bmatrix}$ (Simplify your answers.)

          Let B = \{b_1, b_2\} and C = \{c_1, c_2\} be bases for $\mathbb{R}^2$. Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B.
$\begin{bmatrix} -5\\2 \end{bmatrix}$, $b_2 = \begin{bmatrix} 3\\-1 \end{bmatrix}$, $c_1 = \begin{bmatrix} 1\\2 \end{bmatrix}$, $c_2 = \begin{bmatrix} 1\\1 \end{bmatrix}$
Find the change-of-coordinates matrix from B to C
$P_{C \leftarrow B} = \begin{bmatrix} \Box & \Box\\\Box & \Box \end{bmatrix}$ (Simplify your answers.)

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$Let B = {b1, b2} and C = {c1, c2} be bases for ℝ^2. Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B. < b m a t r i x >, b2 = < b m a t r i x >, c1 = < b m a t r i x >, c2 = < b m a t r i x > Find the change-of-coordinates matrix from B to C PC ← B = < b m a t r i x > (Simplify your answers.)$

Added by Ricardo G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Thanks for your feedback!

Can you solve this question, please? Let B = {bb} and C = {CC} be bases for R2. Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B. Find the change-of-coordinates matrix from B to C. (Simplify your answers.)

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Transcript

00:02 Hello, let's have a look at the question.

00:04 We have been given two bases, b and c and c, and we have been given the values of b1, b2, c1, c2.

00:11 So now we can write capital b as, using the values of b and b1 and b2, we will write minus 1 .7.

00:26 And for c we will write 1 2 comma and 1 1.

00:37 So now we have to find the coordinates from b to c.

00:43 So now let p be the coordinates we have to find.

00:49 Now we have to find b1c and b2c.

00:58 Now let this be the first equation.

01:02 Now first of all let us calculate b1 so now for this we will have the value of b1 is minus 1 and 8 then let a 1 and a 2 be the basis so a 1 and the value of c1 is 1 2 plus a 2 and the value of c2 which is 1 1 1 so now on solving this we will get a 1 and 2 a 1 plus a 2 a 2 8 now adding both these matrices we will get a1 plus a2 and 2 a1 plus a 2 and here we have minus 1 8 now on solving this we can write it as a 1 plus a 2 is equal to minus 1 and 2a1 plus a 2 is equal to 8 so now let us solve this so a 2 will get cancelled out here we will have minus a1 is equal to minus 9 and from here we can get the value of a 1 is equals to 9.

02:18 Now putting the value of a1 equals to 9 in a1 plus a2 equals to minus 1, we will get a2 is to minus.

02:28 Now these are the two values of a1 and a2.

02:32 So from here we can say that base b1 to the c is equals to 9 minus 10.

02:43 Now let this be the second equation.

02:47 Now we will find base to c...

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