Advanced Math Archive: Questions from July 10, 2023
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Let's consider the linear transformation f: R^3 -> R^2 such
that:
F (x, y,z) = (x + z, y - z)
A.- Determine the matrix f with respect to the bases
[V] = {(1,1,1), (1,1,0), (1,0,0)) in R^3
[W] =
Ejercicio 1 Consideremos la transformación lineal \( f: R^{3} \rightarrow R^{2} \) tal que: \[ f(x, y, z)=(x+z, y-z) \] a.- Determine la matriz \( f \) respecto de las bases \[ [v]=\{(1,1,1),(1,1,0),
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Let T
be a linear application of R^2 in itself, such that:
T(1,0) = (1,1) and T(0,1) = (-1,2)
Determine the image of the square of vertices (0,0), (1,0),
(1,1) and (0,1)
Ejercicio 3: Sea T una aplicación lineal de \( R^{2} \) en si mismo, tal que: \[ T(1,0)=(1,1) \text { y } T(0,1)=(-1,2) \] Determine la imagen del cuadrado de vértices \( (0,0),(1,0) .(1,1) \) y \(
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1) Encuentra el área del paralelogramo con vértices A(?4, 6),
B (?2, 9), C (2, 7) y
D (0, 4).
2) Considere los puntos a continuación. P (?2,
0, 0), Q (0, 1, 0), R (0, 0,
3)
(a) Encuentre un vector
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