Question

Let $V = \text{span}(\{\vec{v}_1,\vec{v}_2,\vec{v}_3\})$ be a $3$ dimensional subspace of $\mathbb{R}^4$. Prove that $V^{\perp}$ has dimension $1$.

score 184 · Answer 1 · 2015-11-23 01:00:30

184

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Let $V = \text{span}(\{\vec{v}_1,\vec{v}_2,\vec{v}_3\})$ be a $3$ dimensional subspace of $\mathbb{R}^4$. Prove that $V^{\perp}$ has dimension $1$.

Published on 23 Nov 2015 - 1:00

score 1.6k · Answer 2 · 2026-04-04 03:56:42

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List Question

Let $V = \text{span}(\{\vec{v}_1,\vec{v}_2,\vec{v}_3\})$ be a $3$ dimensional subspace of $\mathbb{R}^4$. Prove that $V^{\perp}$ has dimension $1$.

What is the value of $n$ for which $n!=2^{25} \times 3^{13} \times 5^6 \times 7^4 \times 11^2 \times 13^2 \times 17 \times 19 \times 23 $

Determine how many paths exist from $A$ to $B$ that > travel only to the right and up.

Finding a finite dimensional subspace of an infinite vector space.

Sultan's law involving outnumbering

Finding a basis for the intersection of two vector subspaces.

Find a basis for the hyperplane and use the line to extend the basis for the hyperplane to a basis for $\mathbb{R}^4$

Number of Polynomials with Integer Coefficients that are bounded by $x^2$ and $x^4+1$

How to solve for exponent when adding fractions raised to unknown exponent?

Why is $\left(\frac{1}{2}\right)^{x} = \frac{1}{7}$ the same as saying: $(2)^{x} = 7$

Prove diophantine equation $S^2+R^2+(r_1-r_2)^2 = 2R(r_1+r_2)$ has at most one solution

Clarification on the intended meaning of a probability problem

Proper mathematical description for outer perfect shuffling

Approaching concepts involving graphs in analysis

Working Backwards to Determine Winning Strategy

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