Question

2. Let v be a vector in $\mathbb{R}^n$ and define a function $T_v: \mathbb{R}^n \to \mathbb{R}$ by $T_v(x) = x \cdot v$. (a) Show that $T_v$ is a linear transformation. (b) Find the standard matrix for $T_v$, where $v = (1, 1, 1)$.

          2. Let v be a vector in $\mathbb{R}^n$ and define a function $T_v: \mathbb{R}^n \to \mathbb{R}$ by $T_v(x) = x \cdot v$.
(a) Show that $T_v$ is a linear transformation.
(b) Find the standard matrix for $T_v$, where $v = (1, 1, 1)$.

2. Let v be a vector in ℝ^n and define a function Tv: ℝ^n →ℝ by Tv(x) = x · v.
(a) Show that Tv is a linear transformation.
(b) Find the standard matrix for Tv, where v = (1, 1, 1).

Added by Alfredo R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ekaveera Kumar

Step 1

Additivity: Let x, y be vectors in Rn. Then Ty(x + y) = (x + y)v = xv + yv = Ty(x) + Ty(y). Show more…

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2. Let v be a vector in R and define a function Ty : Rn + R by Ty(x) = x v (a) Show that Ty is a linear transformation. (b) Find the standard matrix for Ty, where v = (1,1,1).