IAS (Admin.) Mains Mathematics: Questions 84 - 89 of 668

Choose Programs:

📹 Video Course 2024 (36 Lectures [25 hrs : 50 mins]): Offline Support

Rs. 160.00 -OR-

1 Month Validity (Multiple Devices)

Preview All LecturesDetails

🎓 Study Material (212 Notes): 2024-2025 Syllabus

Rs. 250.00 -OR-

3 Year Validity (Multiple Devices)

Topic-wise Notes & SampleDetails

🎯 668 Questions (& PYQs) with Full Explanations (2024-2025 Exam)

Rs. 1150.00 -OR-

3 Year Validity (Multiple Devices)

CoverageDetailsSample Explanation

Help me Choose & Register (Watch Video) Already Subscribed?

Question 84

Appeared in Year: 2012

Describe in Detail Subjective▾

Consider the linear mapping by

Find the matrix relative to the basis and the matrix relative to the basis { (1,2) , (2,3) } . (CS main Paper 1)

Edit

Explanation

Given by

And

… (85 more equations) …

Question 85

Appeared in Year: 2012

Describe in Detail Subjective▾

If is a characteristic root of a non-singular matrix , then prove that is a characteristic root of . (CS main Paper 1)

Edit

Explanation

Since is an eigen value of a non-singular matrix

and there exist a non-zero column vector such that

… (15 more equations) …

Question 86

Appeared in Year: 2009

Describe in Detail Subjective▾

Prove that the set of the vectors in which satisfy the equations and is a subspace of . What is the dimension of this subspace find one of its bases. (CS main Paper 1)

Edit

Explanation

Let be the given vector space…

… (590 more equations) …

Question 87

Appeared in Year: 2015

Describe in Detail Subjective▾

Show that the function is harmonic. Find its conjugate harmonic function . Also, find the corresponding analytic function in the terms of Z. (CS main Paper 2)

Edit

Explanation

Given

… (276 more equations) …

Question 88

Appeared in Year: 2012

Describe in Detail Subjective▾

Let be the vector space of all matrices over the field of real numbers.

Let be the set consisting of all matrices with zero determinant. Is a subspace of Justify your Answer. (CS main Paper 1)

Edit

Explanation

lemma: Let be a vector space over a field Then is a subspace of its and

Proof:- Let

… (731 more equations) …

Question 89

Appeared in Year: 2013

Describe in Detail Subjective▾

Let be the linear transformation defined by

Find a basis and the dimension of the image of and the Kernel of . (CS Paper I)

Edit

Explanation

We know that Basis of is

… (1079 more equations) …