Mathematics MCQ - Vectors and Matrices

56 If R=

If then top row of R-1 is

then top row of R-1 is

A
[5 6 4]
B
[5 -3 1]
C
[2 0 1]
D
[2 -1 1/2]

View Explanation
Comment

Since, I R I = 1, therefore top row $\rightarrow$ [5 -3 1]

57 Sum of the eigen values of the matrix

Sum of the eigen values of the matrix

A
5
B
7
C
9
D
18

View Explanation
Comment

Sum of eigen values of given matrix is

= summation of element of diagonal of given matrix

=1 + 5 + 1

= 7

58 For which value of x, will the matrix

For which value of x, will the matrix

become singular

A
4
B
6
C
8
D
12

View Explanation
Comment

For singular matrix,

Linear Algebra

$\Rightarrow$ 8 [0 - 12] - x [0 - 2x12] = 0

$\Rightarrow$ -96 + 24x = 0

$\Rightarrow$ x = 4

59 Rank of the matrix,

A
1
B
2
C
3
D
none of these

View Explanation
Comment

Since,

Linear Algebra

= 12 - 24 + 12 = 0

and M_n = 12 = 0.

Hence rank is 2.

60 Eigen vectors of the matrix

Eigen vectors of the matrix

is (are)

A
(1,0)
B
(0,1)
C
(1,1)
D
(1,-1)

View Explanation
Comment

Eigen value are roots of the equation

Linear Algebra

i.e. (1 - a)² - 1 = 0

$\Rightarrow$ a² - 2a = 0

$\Rightarrow$ a = 0 or a = 2

when a = 0

Linear Algebra

this gives x = y

when a = 2,

Linear Algebra

This gives x = -y

Hence, eigen vectors corresponding to 0 and 2 are

Linear Algebra

Mathematics MCQ - Vectors and Matrices

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