1
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let A = [aij] be a real matrix of order 3 $$\times$$ 3, such that ai1 + ai2 + ai3 = 1, for i = 1, 2, 3. Then, the sum of all the entries of the matrix A3 is equal to :
A
2
B
1
C
3
D
9
2
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
The value of k $$\in$$R, for which the following system of linear equations

3x $$-$$ y + 4z = 3,

x + 2y $$-$$ 3z = $$-$$2

6x + 5y + kz = $$-$$3,

has infinitely many solutions, is :
A
3
B
$$-$$5
C
5
D
$$-$$3
3
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Let $$A = \left[ {\matrix{ 2 & 3 \cr a & 0 \cr } } \right]$$, a$$\in$$R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to :
A
36
B
24
C
45
D
18
4
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Let the system of linear equations

4x + $$\lambda$$y + 2z = 0

2x $$-$$ y + z = 0

$$\mu$$x + 2y + 3z = 0, $$\lambda$$, $$\mu$$$$\in$$R.

has a non-trivial solution. Then which of the following is true?
A
$$\mu$$ = 6, $$\lambda$$$$\in$$R
B
$$\lambda$$ = 3, $$\mu$$$$\in$$R
C
$$\mu$$ = $$-$$6, $$\lambda$$$$\in$$R
D
$$\lambda$$ = 2, $$\mu$$$$\in$$R
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