<span>2x - 3y - 3z = 8
We've been given the normal vector to the plane <2, -3, -3> and a point within the plane (1, -5, 3). In general if you've been given both the normal vector <a,b,c> and a point (e,f,g) within the plane, the expression for the plane will be:
ax + by + cz = d
and you can compute d by:
d = ae + bf + cg
So let's calculate d:
d = ae + bf + cg
d = 2*1 + -3*-5 + -3*3
d = 2 + 15 + -9
d = 8
And the equation for the plane is
2x - 3y - 3z = 8</span>
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
Answer:
-4, 1
Step-by-step explanation:
Answer:
x = -1/2
Step-by-step explanation:
4x - 6 = 10x - 3
+6 +6
4x = 10x + 3
-10x -10x
-6x = 3
/-6 /-6
x = -1/2
If you think about it, 4x7 is half of 8x7 (If you multiply 4, 7, and 2, you get 8x7). So really you can just multiply 4x7 by 2 and you will get 8x7!