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If [(a+b,2),(5,b)]=[(6,2),(5,2)], then t...

If `[(a+b,2),(5,b)]=[(6,2),(5,2)]`, then the value of a is:

A

4

B

2

C

0

D

1

Text Solution

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The correct Answer is:
To solve the equation given by the matrices \([(a+b, 2), (5, b)] = [(6, 2), (5, 2)]\), we will equate the corresponding elements of the two matrices. ### Step-by-Step Solution: 1. **Identify the Corresponding Elements**: From the given matrices, we can equate the elements as follows: - \(a + b = 6\) (from the first row, first column) - \(2 = 2\) (from the first row, second column; this is trivially true) - \(5 = 5\) (from the second row, first column; this is also trivially true) - \(b = 2\) (from the second row, second column) 2. **Substitute the Value of \(b\)**: From the last equation, we have \(b = 2\). We can substitute this value into the first equation: \[ a + b = 6 \implies a + 2 = 6 \] 3. **Solve for \(a\)**: Now, we can isolate \(a\) by subtracting 2 from both sides: \[ a = 6 - 2 \] \[ a = 4 \] ### Final Answer: The value of \(a\) is \(4\).
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