A small airplane takes off from point A and continues to climb upward in a straight line, as shown in the diagram. What is the p
lane’s distance from point A when it reaches point C?
A. 6,900 feet
B. 7,000 feet
C. 11,636 feet
D. 12,600 feet
E. 13,400 feet
A. 6,900 feet
B. 7,000 feet
C. 11,636 feet
D. 12,600 feet
E. 13,400 feet
1 answer:
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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