# Question Bank Solutions for HSC Science (General) 12th Board Exam - Maharashtra State Board - Mathematics and Statistics

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Apply the given elementary transformation of the following matrix.

A = [(1,0),(-1,3)], R1↔ R2

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Concept: Elementry Transformations

Apply the given elementary transformation of the following matrix.

B = [(1,-1,3),(2,5,4)], R1→ R1 – R2

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Apply the given elementary transformation of the following matrix.

A = [(5,4),(1,3)], C1↔ C2; B = [(3,1),(4,5)] R1↔ R2.
What do you observe?

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Concept: Elementry Transformations

Apply the given elementary transformation of the following matrix.

A = [(1,2,-1),(0,1,3)], 2C2

B = [(1,0,2),(2,4,5)], −3R1

Find the addition of the two new matrices.

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Apply the given elementary transformation of the following matrix.

A = [(1,-1,3),(2,1,0),(3,3,1)], 3R3 and then C3 + 2C2

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Concept: Elementry Transformations

Apply the given elementary transformation of the following matrix.

A = [(1,-1,3),(2,1,0),(3,3,1)], 3R3 and then C3 + 2C2

and A = [(1,-1,3),(2,1,0),(3,3,1)], C3 + 2C2 and then 3R3
What do you conclude.

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Apply the given elementary transformation of the following matrix.

Use suitable transformation on [(1,2),(3,4)] to convert it into an upper triangular matrix.

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Apply the given elementary transformation of the following matrix.

Convert [(1,-1),(2,3)] into an identity matrix by suitable row transformations.

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Apply the given elementary transformation of the following matrix.

Transform [(1,-1,2),(2,1,3),(3,2,4)] into an upper triangular matrix by suitable column transformations.

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The total cost of 3 T.V. sets and 2 V.C.R.’s is ₹ 35,000. The shopkeeper wants a profit of ₹ 1000 per T.V. set and ₹ 500 per V.C.R. He sells 2 T.V. sets and 1 V.C.R. and gets the total revenue as ₹ 21,500. Find the cost price and the selling price of a T.V. set and a V.C.R.

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Concept: Elementry Transformations

If A = ((1,0,0),(2,1,0),(3,3,1)), then reduce it to I3 by using column transformations.

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Concept: Elementry Transformations

If A = ((2,1,3),(1,0,1),(1,1,1)), then reduce it to I3 by using row transformations.

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Check whether the following matrix is invertible or not:

((1,0),(0,1))

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Check whether the following matrix is invertible or not:

((1,1),(1,1))

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Check whether the following matrix is invertible or not:

((1,2),(3,3))

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Check whether the following matrix is invertible or not:

((2,3),(10,15))

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Check whether the following matrix is invertible or not:

(("cos" theta , "sin" theta),(- "sin" theta,"cos" theta))

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Check whether the following matrix is invertible or not:

(("sec" theta , "tan" theta),("tan" theta,"sec" theta))

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Check whether the following matrix is invertible or not:

((1,2,3),(2,-1,3),(1,2,3))

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Check whether the following matrix is invertible or not:

((1,2,3),(3,4,5),(4,6,8))

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