Mr. Richard owns an orchard that has a rectagular fence . The orchard is 36 yards long and 18 yards wide . if he walks across th
1 answer:
Answer:
40.2 Yards
Step-by-step explanation:
To find the diagonal length of the orchard, we need to use the Pythagorean Theorem. The formula of the Pythagorean Theorem is:
c²= a² + b²
a = 36 Yards
b = 18 Yards
Now let's plug in our values to the formula.
c² = a² + b²
c² = 36² + 18²
c² = 1296 + 324
c² = 1620
Now to find the value of c we need to get the square root of both sides.
c = 40.2
So the diagonal length of Mr. Richard's orchard is 40.2 Yards.
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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