Find the value of x,y, z

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

Find the value of x,y, z $[\begin{array}{cc} x + 2 & 6 \\ 3 & 5 z \end{array}] = [\begin{array}{cc} 3 & y^{2} + 4 \\ 3 & 20 \end{array}]$

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[\begin{array}{cc} x + 2 & 6 \\ 3 & 5 z \end{array}] = [\begin{array}{cc} 3 & y^{2} + 4 \\ 3 & 20 \end{array}]

Equating the corresponding rows and columns, we get

⇒ x + 2 = 3

⇒ x = 3 – 2 = 1

⇒ 6 = y² + 4

⇒ y² = 6 – 4 = 2

∴ y = \pm \sqrt{2}

5 z = 20 \Rightarrow z = \frac{20}{5} = 4

∴ x = 1, y = \pm \sqrt{2}, z = 4