Given matrices A and B shown below, find (3)A+(8)B.
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Answer:
The values are:
Step-by-step explanation:
Given:
- P = (x₁, y₁, z₁) = (1, 2, b)
- Q = (x₂, y₂, z₂) = (c, -7, 4)
- m = R = (x, y, z) = (-3, a, -1)
To Determine:
a = ?
b = ?
c = ?
Determining the values of a, b, and c
Using the mid-point formula
- As the point R(-3, a, -1) is the midpoint of the line segment jointing the points P(1,2,b) and Q(c,-7,4), so
- m = R = (x, y, z) = (-3, a, -1)
Using the mid-point formula
given
(x₁, y₁, z₁) = (1, 2, b) = P
(x₂, y₂, z₂) = (c, -7, 4) = Q
m = (x, y, z) = (-3, a, -1) = R
substituting the value of (x₁, y₁, z₁) = (1, 2, b) = P, (x₂, y₂, z₂) = (c, -7, 4) = Q, and m = (x, y, z) = (-3, a, -1) = R in the mid-point formula
as (x, y, z) = (-3, a, -1), so
<u>Determining 'c'</u>
-3 = (1+c) / (2)
-3 × 2 = 1+c
<u>Determining 'a'</u>
a = (2+(-7)) / 2
<u>Determining 'b'</u>
-1 = (b+4) / 2
Therefore, the values are: