Let u and v be linearly independent vectors in ℝ 3 , and let P be the plane through u , v , and 0 . The parametric equation of P is x = s u + t v (with s , t in ℝ). Show that a linear transformation T : ℝ 3 ⟶ ℝ 3 maps P onto a plane through 0 , or onto a line through 0 , or onto just the origin in ℝ 3 . What must be true about T ( u ) and T ( v ) in order for the image of the plane P to be a plane?
Let u and v be linearly independent vectors in ℝ 3 , and let P be the plane through u , v , and 0 . The parametric equation of P is x = s u + t v (with s , t in ℝ). Show that a linear transformation T : ℝ 3 ⟶ ℝ 3 maps P onto a plane through 0 , or onto a line through 0 , or onto just the origin in ℝ 3 . What must be true about T ( u ) and T ( v ) in order for the image of the plane P to be a plane?
Solution Summary: The author explains how the linear transformation T:R3to r 3 maps P onto a plane through 0, or onto the origin in .
Let u and v be linearly independent vectors in ℝ3, and let P be the plane through u, v, and 0. The parametric equation of P is x = su + tv (with s, t in ℝ). Show that a linear transformation T : ℝ3 ⟶ ℝ3 maps P onto a plane through 0, or onto a line through 0, or onto just the origin in ℝ3. What must be true about T(u) and T(v) in order for the image of the plane P to be a plane?
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.
High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
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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