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Published on: 23/08/2019
Applications of Matrices and Determinants
Download Tamil Nadu 12th Standard Business Maths and Statistics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Business Maths and Statistics Test
1.
If A, B are two n x n non-singular matrices, then ___________
AB is non-singular
AB is singular
(AB)-1 = A-1 B-1
(AB)-1 does not exit
2.
The value of \(\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right| \)
52
0
513
59
3.
The rank of an n x n matrix each of whose elements is 2 is __________
1
2
n
n2
4.
Rank of a null matrix is _______.
0
-1
\(\infty \)
1
5.
The system of linear equations x + y + z = 2, 2x + y − z = 3, 3x + 2y + k = 4 has unique solution, if k is not equal to _______.
4
0
-4
1
6.
If \(\left| A \right| \neq 0,\) then A is _______.
non-singular matrix
singular matrix
zero matrix
none of these
7.
The system of equations 4x + 6y = 5, 6x + 9y = 7 has _______.
a unique solution
no solution
infinitely many solutions
none of these
8.
Which of the following is not an elementary transformation?
\({ R }_{ i }\leftrightarrow { R }_{ j }\)
\({ R }_{ i }\rightarrow { 2R }_{ i }+{ 2C }_{ j }\)
\({ R }_{ i }\rightarrow { 2R }_{ i }-{ 4R }_{ j}\)
\({ C }_{ i }\rightarrow { C }_{ i }+{ 5C }_{ j }\)
9.
The rank of the unit matrix of order n is ________.
n −1
n
n +1
n2
10.
If A = (1 2 3), then the rank of AAT is ________.
0
2
3
1
11.
If \(\rho (A,B)\neq \rho (A)\) then the system is
12.
For the system of equations AX = B, the solution is X = A-1 B provided
13.
If A is of rank 2, then adj A is of rank
14.
Rank of a zero matrix is
15.
Rank of a matrix
16.
A set of values of the variable x1,x2,...xn satisfying all the equations simultaneously is called__________ of the system
17.
The number of solutions of the system of equations 2x + Y - z = 7, x - 3y + 2z = 1,x + 4y - 3z = 5 is______
18.
If A is a square matrix such that A2 = I, then A-1=_______
19.
If A is a square matrix of order n, then |Adj A|=______
20.
For any 2 x 2 matrix, if A (adj A = \(\left| \begin{matrix} 10 & 0 \\ 0 & 10 \end{matrix} \right| \) then IAI is _______
1.
The non-homogeneous equation are
2x - y + z = 7, 3x + y - 5z = 13, x + y + z = 5
| Augmented matrix [A,B] |
Elementary Transformation |
|---|---|
| \(\left( \begin{matrix} 2 & -1 & 1 \\ 3 & 1 & -5 \\ 1 & 1 & 1 \end{matrix}\begin{matrix} 7 \\ 13 \\ 5 \end{matrix} \right) \) | |
| \(-\left( \begin{matrix} 1 & 1 & 1 \\ 3 & 1 & -5 \\ 2 & -1 & 1 \end{matrix}\begin{matrix} 5 \\ 13 \\ 7 \end{matrix} \right) \) | \({ R }_{ 1 }\leftrightarrow { R }_{ 3 }\) |
| \(\sim \left( \begin{matrix} 1 & 1 & 1 \\ 0 & -2 & -8 \\ 0 & -3 & -1 \end{matrix}\begin{matrix} 5 \\ -2 \\ -3 \end{matrix} \right) \) | \({ R }_{ 2 }\rightarrow { R }_{ 2 }-3{ R }_{ 1 }\) \({ R }_{ 3 }\rightarrow { R }_{ 3 }-2{ R }_{ 1 }\) |
| \(\sim \left( \begin{matrix} 1 & 1 & 1 \\ 0 & -2 & -8 \\ 0 & 0 & 11 \end{matrix}\begin{matrix} 5 \\ -2 \\ 0 \end{matrix} \right) \) | \({ R }_{ 3 }\rightarrow { R }_{ 3 }-\cfrac { 3 }{ 2 } { R }_{ 2 }\) |
Clearly \(\rho (A)=3\) and \(\rho (A,B)\) = 3 = Number of unknowns
\(\therefore\) The given system is consistent and has unique solution.
2.
(b)
0
3.
(a)
1
4.
(a)
0
5.
(b)
0
6.
(a)
non-singular matrix
7.
(b)
no solution
8.
(b)
\({ R }_{ i }\rightarrow { 2R }_{ i }+{ 2C }_{ j }\)
9.
(b)
n
10.
(d)
1
11.
inconsistent
12.
\(|A|\neq 0\)
13.
1
14.
0
15.
\(\ge 0\)
16.
( )
Solution
17.
( )
0
18.
( )
A
19.
( )
|A|n-1
20.
( )
10
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Tamilnadu Stateboard 12th Standard Subjects
Maths
Chemistry
Physics
Biology
Computer Science
Business Maths and Statistics
Economics
Commerce
Accountancy
History
Computer Applications
Biology
Computer Technology
Computer Applications
Computer Science
Business Maths and Statistics
Commerce
Economics
Maths
Chemistry
Physics
Computer Technology
History
Accountancy
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