Question

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

Answer 1

To find the values of a and b, we need to solve the equation PQ = R.

The product of two matrices is obtained by multiplying the corresponding elements and summing the products. In this case, we have:

PQ = (2 -1) * (a b) = (2a - b , -2a + 3b)

Since PQ = R, we have:

2a - b = 2
-2a + 3b = 1

We can solve this system of equations using either substitution or elimination method. Let's use the elimination method:

Multiply the first equation by 3 and the second equation by 2 to make the coefficients of b in both equations cancel out:

6a - 3b = 6
-4a + 6b = 2

Now, add the two equations:

6a - 3b + (-4a + 6b) = 6 + 2
2a + 3b = 8

Now, solve for a:

2a = 8 - 3b
a = (8 - 3b)/2

Substitute this expression for a in the first equation:

2(8 - 3b)/2 - b = 2
8 - 3b - b = 2
-4b = -6
b = -6/-4
b = 3/2 or 1.5

Now, substitute the value of b back into the expression for a:

a = (8 - 3(3/2))/2
a = (8 - 9/2)/2
a = (16/2 - 9/2)/2
a = 7/2 /2
a = 7/4 or 1.75

So, the values of a and b are a = 7/4 or 1.75 and b = 3/2 or 1.5.