In this challenge, you will be given a matrix `A`, a vector `v`, and a scalar `λ`. You will be required to determine if `(λ, v)` is an eigenpair corresponding to `A`; that is, whether or not `Av = λv`.

# Dot Product
The dot product of two vectors is the sum of element-wise multiplication. For example, the dot product of the following two vectors is:

    (1, 2, 3) * (4, 5, 6) = 1*4 + 2*5 + 3*6 = 32

Note that the dot product is only defined between two vectors of the same length.

# Matrix-Vector Multiplication
A matrix is a 2D grid of values. An `m` x `n` matrix has `m` rows and `n` columns. We can imagine an `m` x `n` matrix as `m` vectors of length `n` (if we take the rows).

Matrix-Vector multiplication is defined between an `m` x `n` matrix and a size-`n` vector. If we multiply an `m` x `n` matrix and a size-`n` vector, we obtain a size-`m` vector. The `i`-th value in the result vector is the dot product of the `i`-th row of the matrix and the original vector.

### Example

            1 2 3 4 5
    Let A = 3 4 5 6 7
            5 6 7 8 9

            1
            3
    Let v = 5
            7
            9

If we multiply the matrix and the vector `Av = x`, we get the following:

x<sub>1</sub> = A<sup>T</sup><sub>1</sub> * v `/* AT1 means the first row of A; A1 would be the first column */` = (1,2,3,4,5) * (1,3,5,7,9) = 1*1 + 2*3 + 3*5 + 4*7 + 5*9 = 1+6+15+28+45 = 95

x<sub>2</sub> = A<sup>T</sup><sub>2</sub> * v = (3,4,5,6,7) * (1,3,5,7,9) = 3*1 + 4*3 + 5*5 + 6*7 + 7*9 = 3+12+25+42+63 = 145

x<sub>3</sub> = A<sup>T</sup><sub>3</sub> * v = (5,6,7,8,9) * (1,3,5,7,9) = 5*1 + 6*3 + 7*5 + 8*7 + 9*9 = 5+18+35+56+81 = 195

So, we get `Av = x = (95, 145, 195)`.

# Scalar Multiplication
Multiplication of a scalar (a single number) and a vector is simply element-wise multiplication. For example, `3 * (1, 2, 3) = (3, 6, 9)`. It's fairly straightforward.

# Eigenvalues and Eigenvectors
Given the matrix `A`, we say that `λ` is an eigenvalue corresponding to `v` and `v` is an eigenvector corresponding to `λ` **if and only if** `Av = λv`. (Where `Av` is matrix-vector multiplication and `λv` is scalar multiplication).

`(λ, v)` is an eigenpair.

# Challenge Specifications
### Input
Input will consist of a matrix, a vector, and a scalar. These can be taken in any order in any reasonable format.

### Output
Output will be a truthy/falsy value; truthy if and only if the scalar and the vector are an eigenpair with the matrix specified.

# Rules
- Standard loopholes apply
- If a built-in for verifying an eigenpair exists in your language, you may not use it.
- You may assume that all numbers are integers

# Test Cases

     MATRIX  VECTOR  EIGENVALUE
     2 -3 -1    3
     1 -2 -1    1    1    ->    TRUE
     1 -3  0    0
    
     2 -3 -1    1
     1 -2 -1    1    -2   ->    TRUE
     1 -3  0    1
    
     1  6  3    1
     0 -2  0    0    4    ->    TRUE
     3  6  1    1
    
     1  0 -1    2
    -1  1  1    1    7    ->    FALSE
     1  0  0    0