Question

1. Show that every vector $\begin{bmatrix} x \\ y \end{bmatrix}$ in $\mathbb{R}^2$ can be written as a linear combination of $\begin{bmatrix} 1 \\ 0 \end{bmatrix}$, $\begin{bmatrix} 0 \\ 1 \end{bmatrix}$, and $\begin{bmatrix} 1 \\ 2 \end{bmatrix}$ in infinitely many ways.

Name: 1. Show that every vector in ℝ^2 can be written as a linear combination of , , and in infinitely many ways.
Uploaded: 2022-05-18T19:15:49-08:00
Duration: 3 min 12 s
Channel: Zhumagali Shomanov
Description: 1. Show that every vector in ℝ^2 can be written as a linear combination of , , and in infinitely many ways.

          1. Show that every vector $\begin{bmatrix} x \\ y \end{bmatrix}$ in $\mathbb{R}^2$ can be written as a linear combination of $\begin{bmatrix} 1 \\ 0 \end{bmatrix}$, $\begin{bmatrix} 0 \\ 1 \end{bmatrix}$, and $\begin{bmatrix} 1 \\ 2 \end{bmatrix}$ in infinitely many ways.

1. Show that every vector < b m a t r i x > in ℝ^2 can be written as a linear combination of < b m a t r i x >, < b m a t r i x >, and < b m a t r i x > in infinitely many ways.

Added by Javier J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

05/18/2022

Step 1

Step 1: We want to show that every vector in R2 can be written as a linear combination of (1,0), (0,1), and (1,2) in infinitely many ways. Show more…

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Show that every vector in (x,y) can be written as a linear combination of (1,0) (0,1) and (1,2) in infinitely many ways 1. Show that every vector in R2 can be written as a linear combination of [0] [1]j in infinitely many ways. and