let a beginarray20c 5 and 6 and 1 2 and 1 and 5 endarray

Let \[A = \left[ {\begin{array}{*{20}{c}} 5&6&1\\ 2&{ - 1}&5 \end{array}} \right].\] Let there exist a matrix $$B$$ such that \[AB = \,\left[ {\begin{array}{*{20}{c}} {35}&{49}\\ {29}&{13} \end{array}} \right].\] What is $$B$$ equal to ?

A. \[\left[ {\begin{array}{*{20}{c}} 5&1&4\\ 2&{ 6}&3 \end{array}} \right]\]

B. \[\left[ {\begin{array}{*{20}{c}} 2&6&3\\ 5&{1}&4 \end{array}} \right]\]

C. \[\left[ {\begin{array}{*{20}{c}} 5\\ 1\\ 4 \end{array}\,\,\,\,\,\begin{array}{*{20}{c}} 2\\ 6\\ 3 \end{array}} \right]\]

D. \[\left[ {\begin{array}{*{20}{c}} 2\\ 6\\ 3 \end{array}\,\,\,\,\,\begin{array}{*{20}{c}} 5\\ 1\\ 4 \end{array}} \right]\]

Answer : \[\left[ {\begin{array}{*{20}{c}} 5\\ 1\\ 4 \end{array}\,\,\,\,\,\begin{array}{*{20}{c}} 2\\ 6\\ 3 \end{array}} \right]\]

Solution :
\[\begin{array}{l} A = \left[ {\begin{array}{*{20}{c}} 5&6&1\\ 2&{ - 1}&5 \end{array}} \right]\,\,{\rm{and}}\,{\rm{let}}\,\,B = \left[ {\begin{array}{*{20}{c}} 5\\ 1\\ 4 \end{array}\,\,\,\,\,\begin{array}{*{20}{c}} 2\\ 6\\ 3 \end{array}} \right]\\ \therefore \,AB = \left[ {\begin{array}{*{20}{c}} 5&6&1\\ 2&{ - 1}&5 \end{array}} \right]\,\left[ {\begin{array}{*{20}{c}} 5\\ 1\\ 4 \end{array}\,\,\,\,\,\begin{array}{*{20}{c}} 2\\ 6\\ 3 \end{array}} \right]\\ = \,\left[ {\begin{array}{*{20}{c}} {25 + 6 + 4}&{10 + 36 + 3}\\ {10 - 1 + 20}&{4 - 6 + 15} \end{array}} \right]\\ = \,\left[ {\begin{array}{*{20}{c}} {35}&{49}\\ {29}&{13} \end{array}} \right] \end{array}\]

Releted MCQ Question on
Algebra >> Matrices and Determinants

Releted Question 1

Consider the set $$A$$ of all determinants of order 3 with entries 0 or 1 only. Let $$B$$ be the subset of $$A$$ consisting of all determinants with value 1. Let $$C$$ be the subset of $$A$$ consisting of all determinants with value $$- 1.$$ Then

A. $$C$$ is empty

B. $$B$$ has as many elements as $$C$$

C. $$A = B \cup C$$

D. $$B$$ has twice as many elements as elements as $$C$$

View Answer

Releted Question 2

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then
\[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

A. 0

B. 1

C. $$i$$

D. $$\omega $$

View Answer

Releted Question 3

Let $$a, b, c$$ be the real numbers. Then following system of equations in $$x, y$$ and $$z$$
$$\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - \frac{{{z^2}}}{{{c^2}}} = 1,$$ $$\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1,$$ $$ - \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1$$ has

A. no solution

B. unique solution

C. infinitely many solutions

D. finitely many solutions

View Answer

Releted Question 4

If $$A$$ and $$B$$ are square matrices of equal degree, then which one is correct among the followings?

A. $$A + B = B + A$$

B. $$A + B = A - B$$

C. $$A - B = B - A$$

D. $$AB=BA$$

View Answer

Let \[A = \left[ {\begin{array}{{20}{c}} 5&6&1\\ 2&{ - 1}&5 \end{array}} \right].\] Let there exist a matrix $$B$$ such that \[AB = \,\left[ {\begin{array}{{20}{c}} {35}&{49}\\ {29}&{13} \end{array}} \right].\] What is $$B$$ equal to ?

Releted MCQ Question on
Algebra >> Matrices and Determinants

Consider the set $$A$$ of all determinants of order 3 with entries 0 or 1 only. Let $$B$$ be the subset of $$A$$ consisting of all determinants with value 1. Let $$C$$ be the subset of $$A$$ consisting of all determinants with value $$- 1.$$ Then

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then
\[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

If $$A$$ and $$B$$ are square matrices of equal degree, then which one is correct among the followings?

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Matrices and Determinants

Practice More MCQ Question on Maths Section

Let \[A = \left[ {\begin{array}{*{20}{c}} 5&6&1\\ 2&{ - 1}&5 \end{array}} \right].\] Let there exist a matrix $$B$$ such that \[AB = \,\left[ {\begin{array}{*{20}{c}} {35}&{49}\\ {29}&{13} \end{array}} \right].\] What is $$B$$ equal to ?

Releted MCQ Question on Algebra >> Matrices and Determinants

Consider the set $$A$$ of all determinants of order 3 with entries 0 or 1 only. Let $$B$$ be the subset of $$A$$ consisting of all determinants with value 1. Let $$C$$ be the subset of $$A$$ consisting of all determinants with value $$- 1.$$ Then

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then \[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

If $$A$$ and $$B$$ are square matrices of equal degree, then which one is correct among the followings?

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Practice More MCQ Question on Maths Section

Let \[A = \left[ {\begin{array}{{20}{c}} 5&6&1\\ 2&{ - 1}&5 \end{array}} \right].\] Let there exist a matrix $$B$$ such that \[AB = \,\left[ {\begin{array}{{20}{c}} {35}&{49}\\ {29}&{13} \end{array}} \right].\] What is $$B$$ equal to ?

Releted MCQ Question on
Algebra >> Matrices and Determinants

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then
\[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

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Matrices and Determinants