Let ℰ = { e 1 , e 2 , e 3 } be the standard basis for ℝ 3 , B = { b 1 , b 2 , b 3 } be a basis for a vector space V , and T : ℝ 3 → V be a linear transformation with the property that T ( x 1 , x 2 , x 3 ) = ( x 3 − x 2 ) b 1 − ( x 1 + x 3 ) b 2 + ( x 1 − x 2 ) b 3 a. Compute T ( e 1 ), T ( e 2 ),and T ( e 3 ). b. Compute [T( e 1 )] B , [ T ( e 2 )] B , and [T( e 3 )] B . c. Find the matrix for T relative to ℰ and B .
Let ℰ = { e 1 , e 2 , e 3 } be the standard basis for ℝ 3 , B = { b 1 , b 2 , b 3 } be a basis for a vector space V , and T : ℝ 3 → V be a linear transformation with the property that T ( x 1 , x 2 , x 3 ) = ( x 3 − x 2 ) b 1 − ( x 1 + x 3 ) b 2 + ( x 1 − x 2 ) b 3 a. Compute T ( e 1 ), T ( e 2 ),and T ( e 3 ). b. Compute [T( e 1 )] B , [ T ( e 2 )] B , and [T( e 3 )] B . c. Find the matrix for T relative to ℰ and B .
Let ℰ =
{
e
1
,
e
2
,
e
3
}
be the standard basis for ℝ3, B =
{
b
1
,
b
2
,
b
3
}
be a basis for a vector space V, and T : ℝ3 → V be a linear transformation with the property that
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY