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GATE CS 2021 : Engineering Mathematics Quiz-3 (App update required to attempt this test)

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Question 1

Perform the following operations on the matrix

(i) Add the third row to the second row
(ii) Subtract the third column from the first column.
The determinant of the resultant matrix is ___________.

Question 2

Let U = {1,2,…,𝑛}. Let 𝐴={(𝑥, 𝑋)| 𝑥 𝑋, 𝑋 𝑈}. Consider the following two statements on |𝐴|.

I. |𝐴| = 𝑛2𝑛−1

II.

Which of the above statements is/are TRUE?

Question 3

Two eigen values of a real matrix P are and 3. The determinant of P is _________.

Question 4

If A, B C are square matrices of the same order then  is equal to

Question 5

Suppose that the eigenvalues of matrix A are 1, 2, and 4. The determinant of  (A-1)Tis ____.

Question 6

The following system of equations
x1 + x2 + 2x3 = 1
x1 + 2x2 + 3x3 = 2
x1 + 4x2 + αx3 = 4
has a unique solution. The only possible value(s) for α is/are
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Jun 16GATE & PSU CS