Mathematics Test

If \(A = \left[ {\begin{array}{*{20}{c}} 2&3\\ { - \;1}&2 \end{array}} \right] = \frac{1}{2}\;\left( {P + Q} \right)\) where P is symmetric and Q is skew symmetric matrix then P and Q are ?

\(P = \left[ {\begin{array}{{20}{c}} 4&2\\ 2&4 \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{{20}{c}} 0&4\\ {\;4}&0 \end{array}} \right]\)

\(P = \left[ {\begin{array}{{20}{c}} 4&2\\ 2&4 \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{{20}{c}} 0&4\\ { - \;4}&0 \end{array}} \right]\)

\(P = \left[ {\begin{array}{{20}{c}} 4&2\\ 2&4 \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{{20}{c}} 0&- 4\\ { - \;4}&0 \end{array}} \right]\)

Question 1/10

Only I

Only II

Both I and II

Neither I nor II

Question 2/10

3 × 3

2 × 3

4 × 2

3 × 2

Question 3/10

\(\frac{{3\pi }}{2}\)

π

\(\frac{{\pi }}{3}\)

\(\frac{{\pi }}{6}\)

Question 4/10

A is non-singular

A is singular

A is symmetric

A is skew symmetric

Question 5/10

There exist more than one but finite number of B's such that AB = BA

There exist exactly one B such that AB = BA

There exist infinitely many B's such that AB = BA

There cannot exist any B such that AB = BA

Question 6/10

M2 is non singular

M2 is null matrix

M2 is the identity matrix

M2 is transpose of M1

Question 7/10

-10A

10A

-6A

6A

Question 8/10

(MT)T = M

(cM)T = c(M)T

(M + N)T = MT + NT

MN = NM

Question 9/10

\(P = \left[ {\begin{array}{*{20}{c}} 4&2\\ 2&4 \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{*{20}{c}} 0&4\\ {\;4}&0 \end{array}} \right]\)

\(P = \left[ {\begin{array}{*{20}{c}} 4&2\\ 2&4 \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{*{20}{c}} 0&4\\ { - \;4}&0 \end{array}} \right]\)

\(P = \left[ {\begin{array}{*{20}{c}} 4&2\\ 2&4 \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{*{20}{c}} 0&- 4\\ { - \;4}&0 \end{array}} \right]\)

None of these

Question 10/10

ABC = CBA

(AB)2 = A2B2

AB = 0 ⇒ then always either A = 0 or B = 0

AB = I ⇒ AB = BA

M₂ is non singular

M₂ is null matrix

M₂ is the identity matrix

M₂ is transpose of M₁

(M^T)^T = M

(cM)^T = c(M)^T

(M + N)^T = M^T + N^T

\(P = \left[ {\begin{array}{{20}{c}} 4&2\\ 2&4 \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{{20}{c}} 0&4\\ {\;4}&0 \end{array}} \right]\)

\(P = \left[ {\begin{array}{{20}{c}} 4&2\\ 2&4 \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{{20}{c}} 0&4\\ { - \;4}&0 \end{array}} \right]\)

\(P = \left[ {\begin{array}{{20}{c}} 4&2\\ 2&4 \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{{20}{c}} 0&- 4\\ { - \;4}&0 \end{array}} \right]\)

(AB)² = A²B²