Consider the contrapositive of the statement you want to prove.
The contrapositive of the logical statement
<em>p</em> ⇒ <em>q</em>
is
¬<em>q</em> ⇒ ¬<em>p</em>
In this case, the contrapositive claims that
"If there are no scalars <em>α</em> and <em>β</em> such that <em>c</em> = <em>α</em><em>a</em> + <em>β</em><em>b</em>, then <em>a₁b₂</em> - <em>a₂b₁</em> = 0."
The first equation is captured by a system of linear equations,
or in matrix form,
If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be
and this is what we wanted to prove. QED
Number of cubes increases by 3 for each term.
an= 3n+1
Steps to solve:
25 = x + 19
~Subtract 19 to both sides
6 = x
Best of Luck!
The answer is 2 pounds because 60 times 20 1200 and 1200 divided by 300 is 4 and 1/2 times 4 is 2
Answer:
1, 33.3
2, 81.9
3, 240
4, the farmer sold 33.3 of his crops
5, 750 students are enrolled.