Why it says 'linearly dependent vectors pass through the origin'? Why it must hold? or must it not? Thanks in advance.
2026-02-23 12:02:37.1771848157
Must linearly dependent vectors pass through the origin?
106 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in VECTOR-SPACES
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Does curl vector influence the final destination of a particle?
- Closure and Subsets of Normed Vector Spaces
- Dimension of solution space of homogeneous differential equation, proof
- Linear Algebra and Vector spaces
- Is the professor wrong? Simple ODE question
- Finding subspaces with trivial intersection
- verifying V is a vector space
- Proving something is a vector space using pre-defined properties
- Subspace of vector spaces
Related Questions in LINEAR-INDEPENDENCE
- Let $ \ \large \mathbb{R}[x]_{<4} \ $ denote the space of polynomials in $ \ \mathbb{R} \ $
- Why multiplying a singular Matrix with another vecotr results in null
- Find all $a, b, c$ values which $\sin(ax) , \sin(bx)$ and $\sin(cx)$ are linearly independent
- Exercise 3, Section 6.7 of Hoffman’s Linear Algebra
- Let $\{v_1,..,v_m\}$ and $\{w_1,..,w_n\}$ be linearly independent sets such that $w_j \notin$ span($v_1,..,v_m$), is $v_1,..,v_m,w_1,..,w_n$ lin.ind?
- Show that $\{x_1,...,x_n\}$ are linearly dependent
- Linear dependence of the set of functions $\{\sin^2, \cos^2, 1\}$
- Why matroid cannot have S in I?
- Polynomial linearly dependent
- Algorithm to extend a linearly independent set with unit vectors
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Based on your "vector-spaces" tag, I'm assuming all your vectors in question are really elements of a vector space, say, $\Bbb R^2$.
Recall that when two points live on a line $\ell$ passing through the origin $(0,0)$, then the equation of the line $\ell$ would be of the form: $y=mx$. But this is exactly the condition of two vectors to be linearly dependent. (Why?)
Remark: The above argument does not hold for more than two vectors in general.