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Choose the correct alternative: If A = [cosθsinθ-sinθcosθ] and A(adj A) = kk[k00k], then k = - Mathematics

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प्रश्न

Choose the correct alternative:

If A = `[(costheta, sintheta),(-sintheta, costheta)]` and A(adj A) = `[("k", 0),(0, "k")]`, then k =

पर्याय

  • 0

  • sin θ

  • cos θ

  • 1

MCQ
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उत्तर

1

shaalaa.com
Applications of Matrices: Solving System of Linear Equations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Applications of Matrices and Determinants - Exercise 1.8 [पृष्ठ ४९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 1 Applications of Matrices and Determinants
Exercise 1.8 | Q 15 | पृष्ठ ४९

संबंधित प्रश्‍न

Solve the following system of linear equations by matrix inversion method:

2x – y = 8, 3x + 2y = – 2


Solve the following system of linear equations by matrix inversion method:

2x + 3y – z = 9, x + y + z = 9, 3x – y – z = – 1


Solve the following system of linear equations by matrix inversion method:

x + y + z – 2 = 0, 6x – 4y + 5z – 31 = 0, 5x + 2y + 2z = 13


If A = `[(-5, 1, 3),(7, 1, -5),(1, -1, 1)]` and B = `[(1, 1, 2),(3, 2, 1),(2, 1, 3)]`, Find the products AB and BA and hence solve the system of equations x + y + 2z = 1, 3x + 2y + z = 7, 2x + y + 3z = 2


Four men and 4 women can finish a piece of work jointly in 3 days while 2 men and 5 women can finish the same work jointly in 4 days. Find the time taken by one man alone and that of one woman alone to finish the same work by using matrix inversion method


The prices of three commodities A, B and C are ₹ x, y and z per units respectively. A person P purchases 4 units of B and sells two units of A and 5 units of C. Person Q purchases 2 units of C and sells 3 units of A and one unit of B . Person R purchases one unit of A and sells 3 unit of B and one unit of C. In the process, P, Q and R earn ₹ 15,000, ₹ 1,000 and ₹ 4,000 respectively. Find the prices per unit of A, B and C. (Use matrix inversion method to solve the problem.)


Solve the following systems of linear equations by Cramer’s rule:

`3/2 + 2y = 12, 2/x + 3y` = 13


Solve the following systems of linear equations by Cramer’s rule:

3x + 3y – z = 11, 2x – y + 2z = 9, 4x + 3y + 2z = 25


In a competitive examination, one mark is awarded for every correct answer while `1/4` mark is deducted for every wrong answer. A student answered 100 questions and got 80 marks. How many questions did he answer correctly? (Use Cramer’s rule to solve the problem).


A chemist has one solution which is 50% acid and another solution which is 25% acid. How much each should be mixed to make 10 litres of a 40% acid solution? (Use Cramer’s rule to solve the problem).


A family of 3 people went out for dinner in a restaurant. The cost of two dosai, three idlies and two vadais is ₹ 150. The cost of the two dosai, two idlies and four vadais is ₹ 200. The cost of five dosai, four idlies and two vadais is ₹ 250. The family has ₹ 350 in hand and they ate 3 dosai and six idlies and six vadais. Will they be able to manage to pay the bill within the amount they had?


If ax² + bx + c is divided by x + 3, x – 5, and x – 1, the remainders are 21, 61 and 9 respectively. Find a, b and c. (Use Gaussian elimination method.)


An amount of ₹ 65,000 is invested in three bonds at the rates of 6%, 8% and 9% per annum respectively. The total annual income is ₹ 4,800. The income from the third bond is ₹ 600 more than that from the second bond. Determine the price of each bond. (Use Gaussian elimination method.)


A boy is walking along the path y = ax2 + bx + c through the points (– 6, 8), (– 2, – 12), and (3, 8). He wants to meet his friend at P(7, 60). Will he meet his friend? (Use Gaussian elimination method.)


Choose the correct alternative:

If `("AB")^-1 = [(12, -17),(-19, 27)]` and `"A"^-1 = [(1, -1),(-2, 3)]` then `"B"^-1` =


Choose the correct alternative:

If A = `[(3/5, 4/5),(x, 3/5)]` and AT = A–1, then the value of x is


Choose the correct alternative:

If A = `[(2, 3),(5, -2)]` be such that λA–1 = A, then λ is


Choose the correct alternative:

If 0 ≤ θ ≤ π and the system of equations x + (sin θ)y – (cos θ)z = 0, (cos θ) x – y + z = 0, (sin θ) x + y + z = 0 has a non-trivial solution then θ is


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