Scalar Multiplication of a Matrix
Trending Questions
Q. If A is a skew-symmetric matrix of order 3, then prove that detA=0.
Q. Let A=⎡⎢⎣−3021x5−20x2⎤⎥⎦, B=⎡⎢⎣2b−1⎤⎥⎦ and C=[351]. If tr denotes the trace of a matrix, then the number of integral values of b for which tr(ABC)≤−18 for all x∈R, is
- 3
- 4
- 5
- 6
Q.
Show that the Signum function f:R→R, given by f(x)=⎧⎪⎨⎪⎩1, if x>00, if x=0−1, if x<0 is neither one-one nor onto.
Q. Let A be a non singular, symmetric matrix of order three such that A=adj(A+AT), then
- adj(A−1)=64A
- A−1=A16
- A−1=A64
- adj(A−1)=A1024
Q. If A=[023−4] and kA=[03a2b24], then the values of k, a, b are respectively.
- -6, -12, -18
- -6, 4, 9
- -6, -4, -9
- -6, 12, 18
Q. If A=[100−1] and B=[0110], find AB and BA. Prove that AB≠BA.
Q.
Show that the function defined by g(x)=x-[x] is discontinuous at all integral points. Here, [x] denotes the greatest integer less than or equal to x.
Q. If A=[2−131] and B=[1472], then the value 3A−2B is
- [3−11−4−1]
- [4−1−5−1]
- [4−11−5−1]
- [4−11−3−1]
Q. Simplify
Q. The value of deteminant ∣∣
∣∣a+babaa+ccbcb+c∣∣
∣∣ is equal to
- 4abc
- abc
- a2b2c2
- 4a2bc
Q.
Let A=⎡⎢⎣1sinθ1−sinθ1sinθ−1−sinθ1⎤⎥⎦, where 0≤θ≤2π, then
a) det A=0
b) det Aϵ(2, ∞)
c) det Aϵ(2, 4)
d) det Aε[2, 4]
Q.
Find the matrix X so that X [123446]=[−7−8−9246].
Q. Let A=[1234] and B=[a00b], a, b ∈N. Then
- There does not exist any B such that AB=BA
- There exists more than one but finite number of B′s such that AB=BA
- There exists exactly one B such that AB=BA.
- There exists infinitely many B′s such that AB=BA
Q. If A=[cos2θ−sin2θsin2θcos2θ] and A+AT=I, where I is 2×2 unit matrix and AT is the transpose of A, then the value of θ is equal to
- π6
- π2
- π3
- 3π2
Q. If A=⎡⎢⎣123456710⎤⎥⎦, B=⎡⎢⎣100030045⎤⎥⎦, then Tr(AB) is
Q.
Compute the indicated product.
[3−13−102]⎡⎢⎣2−31031⎤⎥⎦
Q.
Compute the indicated product.
[1−223][123231]
Q.
Simplify :
Q.
Compute the following:
(iii)⎡⎢⎣−14−68516285⎤⎥⎦+⎡⎢⎣1276805324⎤⎥⎦
Q. If and then compute .
Q. Suppose A=[abcd] is a real matrix with nonzero entries, ad–bc=0, and A2=A. Then a+d equals
- 1
- 4
- 3
- 2
Q. If a skew-symmetric matrix of order 2×2 is formed with zero and cube roots of unity, then the determinant of such matrices formed can be
- 0
- 1
- ω
- ω2
Q.
If [xy4z+6x+y]=[8w06] then find the values of x, y, z and w.
Q. If A=[023−4] and kA=[03a2b24], then the values of k, a, b are respectively.
- -6, 12, 18
- -6, -12, -18
- -6, 4, 9
- -6, -4, -9
Q. If m[−3 4]+n[4 −3]=[10 −11], then 3m+7n=
- 5
- 10
- 1
- 3
Q. Multiplication of [411231] with 5 gives
- [2011231]
- [41110155]
- None of the above
- [205510155]
Q. If A=(3376), B=(8709) and C=(2−346), find (A + B)C and AC + BC.
Is (A + B)C = AC + BC?
Is (A + B)C = AC + BC?
Q. Prove that ∣∣
∣∣aa+ba+b+c2a3a+2b4a+3b+2c3a6a+3b10a+6b+3c∣∣
∣∣=a3.
Q. If A=[3a−48], B=[c4−30], C=[−143b] & 3A−2B=6C, find the values of a, b and c.
Q. If [X−Y2−24X6]+[3−2210−1]=[60052X+Y5],
then
then
- X=32
- X=52
- Y=−32
- Y=−52