Finding (x + y) by Equating Matrices
Question:
Find \( (x + y) \) if
\[ \begin{bmatrix} 2x + 1 & 5x \\ 0 & y^2 + 1 \end{bmatrix} = \begin{bmatrix} x + 3 & 10 \\ 0 & 26 \end{bmatrix} \]
Concept Used
Two matrices are equal if their corresponding elements are equal.
Step 1: Equate Corresponding Elements
\[ 2x + 1 = x + 3 \quad …(1) \]
\[ 5x = 10 \quad …(2) \]
\[ y^2 + 1 = 26 \quad …(3) \]
Step 2: Solve for x
From (2):
\[ 5x = 10 \Rightarrow x = 2 \]
Check in (1):
\[ 2(2)+1 = 5,\quad 2+3 = 5 ✔ \]
Step 3: Solve for y
From (3):
\[ y^2 + 1 = 26 \Rightarrow y^2 = 25 \Rightarrow y = \pm 5 \]
Step 4: Find (x + y)
\[ x + y = 2 + 5 = 7 \] or \[ x + y = 2 – 5 = -3 \]
Final Answer
\[ x + y = 7 \quad \text{or} \quad -3 \]