Question

For what values ​​of a, b, c and d the following matrix equation is met:

(1 C02 (1c0 19 15 -3 a-3 1 -3 a -3 1 = 40 40 0 bd 6) bd 6) 13 - 15 19

a=__________ ; b= ________ ; c=_________ and d=_________

Answer 1

To find values of a,b,c and d :

                                             (1)

11 a To c -3 d ol ² 1 6) - 3 11 a 16 c 3 d ol 1 6) = /19 40 (13 15 40 - 15 -3) 0 19)

Solution:
Step 1:

      (2)

11 a 16 c -3 d ol 1) 6 = 11 a 16 c -3 d ol 1 6 11 a 16 c -3 d ol 1 6) / ac +1 = | b-2a 7b + ad -2cc ac + d +9 3 bc + 3d d +36)

Step 2:

                                         (3)

1 —3 |a \ь с — 3 d 0\ 1 — 3 1) = 1 — 3а 6) — 36 — 3со 9 — 3 — 3d -18)

Step 3:

Adding (2) & (3), we get:

                        (4)

c 71 a To c -3 d ol 1 6) -3 1 a 16 c ol -3 1] = d 6) I ac - 2 b - 5a 4b + ad -5c ac + d + 18 bcd 0 +18)

Step 4:
Equating RHS of (1) & (4), we get:

ac - 2 = 19

So,

ac = 21                             (5)

- 5c = 15

So,

c = - 3                              (6)

Substituting in (5), we get:

a = - 7                              (7)

b - 5a = 40                        (8)

Substituting (7), we get:

b = 5                                (9)

ac+d+18 = 40                  (10)

Substituting (7) & (6), we get:

d = 1                              (11)
Thus, the solution is:

a = - 7

b = 5

c = - 3

d = 1