Let A be a 2 × 2 real matrix with entries from {0, 1} and |A| 0. Consider the following two statements;
(P)If A I2, then |A| = – 1
(Q)If |A| = 1, then tr(A) = 2
where I2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then :
(P) is true and (Q) are false
Both (P) and (Q) are true
Both (P) and (Q) are false
(P) is false and (Q) is true
Let A = {x = (x, y, z)T : PX = 0 and x2 + y2 + z2 = 1}, where P then the set A
is a singleton
contains more than two elements
contains exactly two elements
is an empty set.
Let a, b, c R be all non-zero satisfy a3 + b3 + c3 = 2.If the matrix A = satifies ATA = I, then a value of abc can be :
3
If a + x = b + y = c + z + 1, where a, b, c, x, y, z are non–zero distinct real numbers then
y(a - b)
0
y(b - a)
y(a - c)
Let m and M be respectively the minimum and maximum value values of
Then the ordered pair (m, M) = ?
( - 3, 3)
(1, 3)
( - 3, - 1)
( - 4, - 1)