Question

Solve the equation for x, y, z and t,

if, 2\(\left[\begin{array}{ll} x & z \\ y & t \end{array}\right]\)+3\(\left[\begin{array}{ll} 1 & -1 \\ 0 & 2 \end{array}\right]\) = 3\(\left[\begin{array}{ll} 3 & 5 \\ 4 & 6 \end{array}\right]\).

Answer 1

2\(\left[\begin{array}{ll} x & z \\ y & t \end{array}\right]\)+3\(\left[\begin{array}{ll} 1 & -1 \\ 0 & 2 \end{array}\right]\) = 3\(\left[\begin{array}{ll} 3 & 5 \\ 4 & 6 \end{array}\right]\)

or \(\left[\begin{array}{ll} 2x & 2z \\ 2y & 2t \end{array}\right]\)+\(\left[\begin{array}{ll} 3 & -3 \\ 0 & 6 \end{array}\right]\) = \(\left[\begin{array}{ll} 9 & 15 \\ 12 & 18 \end{array}\right]\)

or \(\left[\begin{array}{cc} 2 x+3 & 2 z-3 \\ 2 y & 2 t+6 \end{array}\right]\) = \(\left[\begin{array}{cc} 9 & 15 \\ 12 & 18 \end{array}\right]\).

Equating corresponding elements, we get:

2x + 3 = 9 or 2x = 9 – 3 = 6. ∴ x = 3.

2y = 12 ∴ y = 6.

2z – 3 = 15 or 2z – 15 + 3 = 18 ∴ z = 9.

2t + 6 = 18 or 2t = 18 – 6 = 12 ∴ t = 6.

Thus, x = 3, y = 6, z = 9 and t = 6.