Find 3 consecutive even integers such that the sum of twice the smallest number and 3 times the largest is 42

Mathematics

1 answer:

nadya68 [22]3 years ago

6 0

integers n, n+2 , n+4

2n + 3(n+4) = 42

2n + 3n +12 = 43

5n +12 = 42

5n = 30

n = 6

integers 6, 8 ,10

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For what values of h are the vectors [Start 3 By 1 Matrix 1st Row 1st Column negative 1 2nd Row 1st Column 4 3rd Row 1st Column

Bogdan [553]

Answer:

The set is linearly dependent for every value of h.

Step-by-step explanation:

Recall that a set of vector {a,b,c,d} is a linearly dependent set of vectors if any of the vectors can be written as a linear combination of the other ones.

We are given the following vectors.a=(-1,4,6), b=(5,2,-3), c=(3,-5,-4), d=(12,-20, h). At first, we will check if a,b,c are linearly independent. To do so, we will calculate the following determinant (the procedure of the calculation is omitted).

$\left|\begin{matrix}-1 & 5 & 3 \\ 4 & 2 & -5 & \\ 6 & -3 & -4\end{matrix}\right| = -119\neq 0$

Since the determinant is not zero, this implies that the vectors a,b,c are all linearly independent. Since a,b,c are all vectors in $\mathbb{R}^3$ which is a 3-dimensional space, and they are 3 linear independent vectors, then they are automatically a base of this space. Consider now the vector d. Since {a,b,c} is a base of $\mathbb{R}^3$ , then it generates any vector of this space(i.e any other vector of the space is a linear combination of {a,b,c}). In particular, d. So the set {a,b,c,d} is linearly independent for any value of h