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Find the value of a, b, c and d from the equation: [(a – b, 2a + c),(2a – b, 3c + d)] = [(–1, 5),(0, 13)]

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प्रश्न

Find the value of a, b, c and d from the equation:

`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`

योग
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उत्तर

`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`

As the two matrices are equal, their corresponding elements are also equal.

Comparing the corresponding elements, we get:

a – b = –1   ...(1)

2a – b = 0   ...(2)

2a + c = 5   ...(3)

3c + d = 13   ...(4)

From (2), we have:

b = 2a

Then, from (1), we have:

a – 2a = –1

⇒ a = 1

⇒ b = 2

Now, from (3), we have:

2 × 1 + c = 5

⇒ c = 3

From (4) we have:

3 × 3 + d = 13

⇒ 9 + d = 13

⇒ d = 4

∴ a = 1, b = 2, c = 3 and d = 4

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अध्याय 3: Matrices - EXERCISE 3.1 [पृष्ठ ४२]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 3 Matrices
EXERCISE 3.1 | Q 7. | पृष्ठ ४२

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