HSC Commerce इयत्ता १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Find the rank of the following matrices

`((1, 2, -1, 3),(2, 4, 1, -2),(3, 6, 3, -7))`

Find the rank of the following matrices

`((3, 1, -5, -1),(1, -2, 1, -5),(1, 5, -7, 2))`

Find the rank of the following matrices

`((1, -2, 3, 4),(-2, 4, -1, -3),(-1, 2, 7, 6))`

If A = `((1, 1, -1),(2, -3, 4),(3, -2, 3))` and B = `((1, -2, 3),(-2, 4, -6),(5, 1, -1))`, then find the rank of AB and the rank of BA.

Solve the following system of equations by rank method

x + y + z = 9, 2x + 5y + 7z = 52, 2x – y – z = 0

Show that the equations 5x + 3y + 7z = 4, 3x + 26y + 2z = 9, 7x + 2y + 10z = 5 are consistent and solve them by rank method

Show that the following system of equations have unique solutions: x + y + z = 3, x + 2y + 3z = 4, x + 4y + 9z = 6 by rank method

For what values of the parameter λ, will the following equations fail to have unique solution: 3x – y + λz = 1, 2x + y + z = 2, x + 2y – λz = – 1

The price of three commodities, X, Y and Z are and z respectively Mr. Anand purchases 6 units of Z and sells 2 units of X and 3 units of Y. Mr.Amar purchases a unit of Y and sells 3 units of X and 2 units of Z. Mr. Amit purchases a unit of X and sells 3 units of Y and a unit of Z. In the process they earn ₹ 5,000/-, ₹ 2,000/- and ₹ 5,500/- respectively. Find the prices per unit of three commodities by rank method

An amount of ₹ 5,000/- is to be deposited in three different bonds bearing 6%, 7% and 8% per year respectively. Total annual income is ₹ 358/-. If the income from the first two investments is ₹ 70/- more than the income from the third, then find the amount of investment in each bond by the rank method

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A = (1, 2, 3), then the rank of AA^T is

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The rank of m n × matrix whose elements are unity is

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If A = `((2, 0),(0, 8))`, then p(A) is

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The rank of the matrix `((1, 1, 1),(1, 2, 3),(1, 4, 9))` is

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The rank of the unit matrix of order n is

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If p(A) = r then which of the following is correct?

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If A = `((1),(2),(3))` then the rank of AA^T is

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If the rank of the matrix `[(lambda, -1, 0),(0, lambda, -1),(-1, 0, lambda)]` is 2, then λ is

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The rank of the diagonal matrix `[(1, , , , ,),(, 2, , , ,),(, , -3, , ,),(, , , 0, ,),(, , , , 0,),(, ,  , , ,0)]`

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Which of the following is not an elementary transformation?