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

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

Solve the equation for x, y, z and t, if
$2 [\begin{array}{cc} x & z \\ y & t \end{array}] + 3 [\begin{array}{cc} 1 & - 1 \\ 0 & 2 \end{array}] = 3 [\begin{array}{cc} 3 & 5 \\ 4 & 6 \end{array}]$

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$[\begin{array}{cc} 2 x & 2 z \\ 2 y & 2 t \end{array}] + [\begin{array}{cc} 3 & - 3 \\ 0 & 6 \end{array}] = [\begin{array}{cc} 9 & 15 \\ 12 & 18 \end{array}]$

2x + 3 = 9 ⇒ 2x = 6 ∴ x = 3
2z – 3 = 15 ⇒ 2z = 18 ∴ z = 9

2y + 0 = 12 ⇒ 2y = 12 ∴ y = 6

2y + 6 = 18 ⇒ 2t = 12 ∴ x = 6