7.Find the value of a, b, c and d from the equation:2a-b 3c+d0 13
The given equation is,
[ a − b 2 a + c 2 a − b 3 c + d ] = [ − 1 5 0 13 ]
Since the given matrices are equal, their corresponding elements will be also equal.
a − b = − 1 (1)
2 a + c = 5 (2)
2 a − b = 0 (3)
3 c + d = 13 (4)
Solve equation (3), we get:
2 a − b = 0 b = 2 a (5)
By substituting b = 2 a in equation (1), we get:
a − b = − 1 a − 2 a = − 1 a = 1
By substituting the value of a in equation (5), we get:
b = 2 a = 2 × 1 = 2
By substituting the value of a in equation (2), we get:
2 a + c = 5 2 × 1 + c = 5 c = 5 − 2 = 3
By substituting the value of c in equation (4), we get:
3 c + d = 13 3 × 3 + d = 13 d = 13 − 9 = 4
Thus, the required values are a = 1 , b = 2 , c = 3 and d = 4 .
The given equation is,
Since the given matrices are equal, their corresponding elements will be also equal.
Solve equation (3), we get:
By substituting
By substituting the value of
By substituting the value of
By substituting the value of
Thus, the required values are
