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.
11. Let / be the intersection of the two planes
2x - 3y + 4z = 2 and x-z=1
a. Find a vector equation of 1.
b. Find an equation of the plane that is perpendicular to /
and contains the point (-9, 12, 14).
Let the solid form in the orthogonal coordinate system xyz be surrounded by points A, B, C, D and F, where A = (-4, 1, 3), B = (6, 1, 1), C = ( 9, 5, 0), D = (4, 5, 1), E = (5, 3, 8) and F is the midpoint of the line BD as shown in Figure
1. Find the value of alpha where alpha is the angle between the vectors. FA and FB, where 0 < alpha < Pi. Consider alpha an acute or obtuse angle and justify it.
2. Find at least one pair of perpendicular vectors, rationalize and demonstrate
3. Find at least one pair of parallel vectors, reasoning and demonstrating that their solutions must not be the same or negated. And there must be a beginning and an end of the vector. is the point set
Map the straight line joining A (-2 + j3) and B (1 + j2) in the z-plane
onto the w-plane using the transformation w= (-3 +j)z+ (2 + j4). State
the magnification, rotation, and translation.
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