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TN 11th Tamil இயற்கை வேளாண்மை,சுற்றுச்சூழல் -செய்யுள் - மனோன்மணீயம் Important Questions And Answers Study Material - QB365 Set A
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Published on: 28/08/2019
Matrices and Determinants
Download Tamil Nadu 11th Standard Maths 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 Maths Test1.
If f(x) = \(\left| \begin{matrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{matrix} \right| \) then _____________
f(a) = 0
f(b) = 0
f(0) = 0
f(1) = 0
2.
If \(\left( \begin{matrix} 2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{matrix} \right) \) is a singular matrix, then \(\lambda \) is_____________
\(\lambda \)=2
\(\lambda \)≠2
\(\lambda =\frac { -8 }{ 5 } \)
\(\lambda \neq \frac { -8 }{ 5 } \)
3.
The value of\(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+sin\theta & 1 \\ 1 & 1 & 1+cos\theta \end{matrix} \right| \) is _____________
3
1
2
\(\frac{1}{2}\)
4.
On using elementary row operation R1⟶R1-3R2 in the following matrix equation \(\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)________.
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} -1 & -3 \\ 1 & 1 \end{pmatrix}\)
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 1 & -7 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
\(\begin{pmatrix} 4 & 2 \\ -5 & -7 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ -3 & -3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
5.
If \(\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}\), then the value of x+y is _________ .
5
6
4
3
6.
The product of any matrix by the scalar_________is the null matrix.
1
0
I
matrix itself
7.
If A =\(\begin{bmatrix} 1& 2 &2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}\) is a matrix satisfying the equation AAT = 9I, where I is 3 \(\times\) 3 identity matrix, then the ordered pair (a, b) is equal to
(2, - 1)
(- 2, 1)
(2, 1)
(- 2, - 1)
8.
If A = \(\begin{bmatrix}\lambda & 1 \\ -1 & -\lambda \end{bmatrix}\), then for what value of \(\lambda\), A2 = O?
0
\(\pm 1\)
-1
1
9.
Which one of the following is not true about the matrix \(\begin{bmatrix} 1 &0 &0 \\ 0 & 0 &0 \\ 0 & 0 & 5 \end{bmatrix}?\)
a scalar matrix
a diagonal matrix
an upper triangular matrix
a lower triangular matrix
10.
If aij = \({1\over2}(3i-2j)\) and A = [aij]2x2 is
\(\begin{bmatrix} {1\over 2}& 2 \\ -{1\over2} & 1 \end{bmatrix}\)
\(\begin{bmatrix} {1\over 2}& -{1\over2} \\ 2& 1 \end{bmatrix}\)
\(\begin{bmatrix} 2& 2\\ {1\over 2}& -{1\over2} \end{bmatrix}\)
\(\begin{bmatrix} -{1\over 2}& {1\over2} \\ 1& 2 \end{bmatrix}\)
1.
(d)
f(1) = 0
2.
(c)
\(\lambda =\frac { -8 }{ 5 } \)
3.
(d)
\(\frac{1}{2}\)
4.
(a)
\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)
5.
(d)
3
6.
(b)
0
7.
\(A A^{T}=9 I \)
\({\left[\begin{array}{ccc} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{array}\right]\left[\begin{array}{ccc} 1 & 2 & a \\ 2 & 1 & 2 \\ 2 & -2 & b \end{array}\right]=\left[\begin{array}{ccc} 9 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 9 \end{array}\right]} \)
\({\left[\begin{array}{ccc} 1+4+4 & 2+2-4 & a+4+2 b \\ 2+2-4 & 4+1+4 & 2 a+2-2 b \\ a+4+2 b & 2 a+2-2 b & a^{2}+4+b^{2} \end{array}\right]} \)
\(=\left[\begin{array}{ccc} 9 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 9 \end{array}\right] \)
\(a+4+2 b =0 \)
\(a+2 b =-4 \)
\(2 a-2 b+2 =0 \)
\(2 a-2 b =-2 \)
\(\text { Solve (1) } \&(2) \text { we get } a=-2 b=-1\)
\(\therefore(a, b)=(-2,1)\)
8.
\(A^{2}=A \times A=\left[\begin{array}{cc} \lambda & 1 \\ -1 & -\lambda \end{array}\right]\left[\begin{array}{cc} \lambda & 1 \\ -1 & -\lambda \end{array}\right]\)
\(=\left[\begin{array}{cc} \lambda^{2}-1 & \lambda-\lambda \\ -\lambda+\lambda & -1+\lambda^{2} \end{array}\right]=0\)
\(\therefore \lambda^{2} =1 \)
\(\lambda =\pm 1\)
9.
(a)
a scalar matrix
10.
\(A=\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right] \)
\(a_{11}=\frac{1}{2}(3-2)=\frac{1}{2} ; a_{12}=\frac{1}{2}(3-4)=\frac{-1}{2} \)
\(a_{21}=\frac{1}{2}(3(2)-2)=\frac{4}{2}=2 ; a_{22}=\frac{1}{2}(6-4)=\frac{2}{2}=1 \)
\(\therefore A=\left[\begin{array}{ll} \frac{1}{2} & -\frac{1}{2} \\ 2 & 1 \end{array}\right] \)
11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - காவடிச்சிந்து Important Questions And Answers Study Material - QB365 Set A
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TN 11th Tamil மாமழை போற்றுதும் - செய்யுள் - ஐங்குறுநூறு Important Questions And Answers Study Material - QB365 Set A
Tamilnadu Stateboard 11th Standard Subjects
Maths
Commerce
Economics
Biology
Business Maths and Statistics
Accountancy
Computer Science
Physics
Chemistry
Maths
Biology
Economics
Physics
Chemistry
History
Business Maths and Statistics
Computer Science
Accountancy
Computer Applications
History
Computer Technology
Commerce
Computer Applications
Computer Technology
Tamil
English
French
Tamilnadu Stateboard Standards
