Question

A matrix P (2 -1),Q(a) and R(2).Find the values
-4 3. b. 1.
of a and b given that PQ=R

Answer 1

To find the values of a and b, we can multiply matrices P and Q and equate it to matrix R.

We have matrix P as:
P = (2 -1)
(-4 3)

Matrix Q has one unknown value a:
Q = (a)
(b)

When we multiply matrices P and Q, we get:
PQ = (2a - b -a + 3b)
(-4a + 3b -4a + 9b)

We are given that PQ is equal to matrix R:
PQ = (2 -1)
(-4 3)

Equating corresponding elements, we get the following equations:
2a - b = 2 ----(1)
-a + 3b = -1 ----(2)
-4a + 3b = -4 ----(3)
-4a + 9b = 3 ----(4)

To solve these equations, we can use the method of substitution or elimination.

From equation (2), we get a = 3b - 1. Substituting this value in equation (1), we have:
2(3b - 1) - b = 2
6b - 2 - b = 2
5b - 2 = 2
5b = 4
b = 4/5

Substituting b = 4/5 in equation (2), we have:
-a + 3(4/5) = -1
-a + 12/5 = -1
-a = -1 - 12/5
-a = -5/5 - 12/5
-a = -17/5
a = 17/5

Therefore, the values of a and b are a = 17/5 and b = 4/5, respectively.