If a sample of 58 runners were taken from a population of 302 runners
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As an example, let's invert the matrix
We construct the augmented matrix,
On this augmented matrix, we perform row operations in such a way as to transform the matrix on the left side into the identity matrix, and the matrix on the right will be the inverse that we want to find.
Now we can carry out Gaussian elimination.
• Eliminate the column 1 entry in row 2.
Combine 2 times row 1 with 3 times row 2 :
2 (-3, 2, 1, 1, 0, 0) + 3 (2, 1, 1, 0, 1, 0)
= (-6, 4, 2, 2, 0, 0) + (6, 3, 3, 0, 3, 0)
= (0, 7, 5, 2, 3, 0)
which changes the augmented matrix to
• Eliminate the column 1 entry in row 3.
Using the new aug. matrix, combine row 1 and 3 times row 3 :
(-3, 2, 1, 1, 0, 0) + 3 (1, 1, 1, 0, 0, 1)
= (-3, 2, 1, 1, 0, 0) + (3, 3, 3, 0, 0, 3)
= (0, 5, 4, 1, 0, 3)
• Eliminate the column 2 entry in row 3.
Combine -5 times row 2 and 7 times row 3 :
-5 (0, 7, 5, 2, 3, 0) + 7 (0, 5, 4, 1, 0, 3)
= (0, -35, -25, -10, -15, 0) + (0, 35, 28, 7, 0, 21)
= (0, 0, 3, -3, -15, 21)
• Multiply row 3 by 1/3 :
• Eliminate the column 3 entry in row 2.
Combine row 2 and -5 times row 3 :
(0, 7, 5, 2, 3, 0) - 5 (0, 0, 1, -1, -5, 7)
= (0, 7, 5, 2, 3, 0) + (0, 0, -5, 5, 25, -35)
= (0, 7, 0, 7, 28, -35)
• Multiply row 2 by 1/7 :
• Eliminate the column 2 and 3 entries in row 1.
Combine row 1, -2 times row 2, and -1 times row 3 :
(-3, 2, 1, 1, 0, 0) - 2 (0, 1, 0, 1, 4, -5) - (0, 0, 1, -1, -5, 7)
= (-3, 2, 1, 1, 0, 0) + (0, -2, 0, -2, -8, 10) + (0, 0, -1, 1, 5, -7)
= (-3, 0, 0, 0, -3, 3)
• Multiply row 1 by -1/3 :
So, the inverse of our matrix is
The perpendicular bisector theorem gives the statements that ensures
that and
are perpendicular.
The two statements if true that guarantee is perpendicular to line
are;
Reasons:
The given diagram is the construction of the line perpendicular to line
.
Required:
The two statements that guarantee that is perpendicular to line
.
Solution:
From the point <em>C</em> arcs <em>E</em> and <em>D</em> are drawn to cross line , therefore;
arcs drawn from the same radius.
is perpendicular to line
, given.
Therefore;
by perpendicular bisector theorem.
Learn more about the perpendicular bisector theorem here:
