# Plus Two Maths Chapter Wise Previous Questions Chapter 3 Matrices

Kerala State Board New Syllabus Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 3 Matrices.

## Kerala Plus Two Maths Chapter Wise Previous Questions Chapter 3 Matrices

### Plus Two Maths Matrices 3 Marks Important Questions

Question 1.
Write A as the sum of a symmetric and a skew-symmetric matrix. $$A=\left[\begin{array}{ccc} 1 & 4 & -1 \\ 2 & 5 & 4 \\ -1 & -6 & 3 \end{array}\right]$$ (March – 2010)

Question 2.
Consider the matrices
$$A=\left[\begin{array}{lll} 2 & 1 & 3 \\ 2 & 3 & 1 \\ 1 & 1 & 1 \end{array}\right] \text { and } B=\left[\begin{array}{ccc} -1 & 2 & 3 \\ -2 & 3 & 1 \\ -1 & 1 & 1 \end{array}\right]$$
(i) Find A+B
(ii) Find (A + B) (A-B) (May -2010)

Question 3.
Given $$P=\left[\begin{array}{cc} 2 & -3 \\ -1 & 2 \end{array}\right]$$ Find the inverse of P by elementary row operation. (March 2011)

Question 4.
Let $$A=\left[\begin{array}{lll} 3 & 6 & 5 \\ 6 & 7 & 8 \end{array}\right] \text { and } C=\left[\begin{array}{ccc} 1 & 2 & -3 \\ 4 & 5 & 6 \end{array}\right]$$

(i) Find 2A
(ii) Find the matrix B such that 2A + B = 3C (May 2011)

Question 5.
Let $$A=\left[\begin{array}{cc} 2 & 4 \\ -1 & 1 \end{array}\right]$$
(i) Apply elementary transformation R → R R1/2 in the matrix A.
(ii) Find the inverse of A by the elementary transformation. (May 2011)

Question 6.
Consider the matrix $$A=\left[\begin{array}{cc} 3 & 1 \\ -1 & 2 \end{array}\right]$$
(i) Find A2
(ii) Find ksothat A2 = kA – 7I (March – 2012)

Question 7.
Consider a 2×2 matrix
$$A=\left[a_{i j}\right] where a_{i j}=|2 i-3 j|$$
(i) Write A
(ii) Find A + AT (March – 2012)

Question 8.
If $$A=\left[\begin{array}{cc} 3 & 1 \\ -1 & 2 \end{array}\right]$$ then
(i) Find A2
(ii) Hence show that A2 – 5A + 7I = 0. (March 2013)

Question 9.
If a matrix $$A=\left[\begin{array}{ll}3 x & x \\ -x & 2 x\end{array}\right]$$ is a solution of the equation x2 – 5x + 7 = 0, find any one value of X. (May 2013)

Question 10.
Consider the matrices $$A=\left[\begin{array}{cc}1 & -2 \\ -1 & 3\end{array}\right] and B=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$$ $$A B=\left[\begin{array}{ll}2 & 9 \\ 5 & 6\end{array}\right]$$, find the values of a,b,c,d (March – 2014)

Question 11.
Consider a 2 x 2 matrix A=[aij] Where $$a_{i j}=\frac{(i+2 j)^{2}}{2}$$
(i) Write A
(ii) Find A + AT (March – 2014)

Question 12.
If X + Y = $$\left[\begin{array}{ll}7 & 0 \\ 2 & 5\end{array}\right]$$ and X – Y = $$\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]$$ then
(i) Find X and Y.
(ii) Find 2X + Y. (May – 2014)

Question 13.
i) If A, B are symmetric matrices of same order then AB – BA is always a ………….
A) Skew-Symmetric matrix
B) Symmetric matrix
C) Identity matrix
D) Zero matrix
(ii) For the matrix $$A=\left[\begin{array}{ll}2 & 4 \\ 5 & 6\end{array}\right]$$, verify that A + AT is a symmetric matrix. (March – 2015)

Question 14.
Consider the matrix $$A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$$
(i) Find A2
(ii) Find k so that A2 = kA – 21 (May – 2015)

### Plus Two Maths Matrices 4 Marks Important Questions

Question 1.
(i) Find the value of x and y from the equations $$a\left[\begin{array}{cc}x & 5 \\ 7 & y-3\end{array}\right]+\left[\begin{array}{cc}3 & -4 \\ 1 & 2\end{array}\right]=\left[\begin{array}{cc}7 & 6 \\ 15 & 14\end{array}\right]$$
(ii) Given $$A=\left[\begin{array}{cc}1 & 2 \\ 3 & -1 \\ 4 & 2\end{array}\right], B=\left[\begin{array}{ccc}-1 & 4 & -5 \\ 2 & 1 & 0\end{array}\right]$$ Show that AB ≠ BA (March – 2011)

Question 2.
(i) Find a, b matrix $$\left[\begin{array}{ccc}0 & 3 & a \\ b & 0 & -2 \\ 5 & 2 & 0\end{array}\right]$$ is skew symmetric matrix.
(ii) Express $$A=\left[\begin{array}{ccc}7 & 3 & -5 \\ 0 & 1 & 5 \\ -2 & 7 & 3\end{array}\right]$$ sum of a symmetric and a skew symmetric matrix. (May – 2012)

Question 3.
Consider the matrices $$A=\left[\begin{array}{cc}2 & -6 \\ 1 & 2\end{array}\right] and A+3 B=\left[\begin{array}{cc}5 & -3 \\ -2 & -1\end{array}\right]$$
(i) Find matrix B
(il) Find matrix AB.
(iii) Find the transpose of B. (May – 2013)

Question 4.
(i) The value of k such that matrix $$\left[\begin{array}{cc} 1 & k \\ -k & 1 \end{array}\right]$$ is symmetric if
(a) 0
(b) 1
(c) – 1
(d) 2

(ii) If $$A=\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$ then prove that $$A^{2}=\left[\begin{array}{cc} \cos 2 \theta & \sin 2 \theta \\ -\sin 2 \theta & \cos 2 \theta \end{array}\right]$$
$$\text { (iii) if } A=\left[\begin{array}{ll} 1 & 3 \\ 4 & 1 \end{array}\right], \text { then find }\left|3 A^{T}\right|$$ (March – 2017)

### Plus Two Maths Matrices 6 Marks Important Questions

Question 1.
Let A be a matrix of order 3 x 3 whose elements are given by aij = 21 – j
(i) Obtain the matrix A.
(ii) Find AT Also express A as the sum of symmetric and skew-symmetric matrix. (March – 2010)

Question 2.
Consider a 2 x 2 matrix $$A=\left[a_{\theta}\right]$$ with aij = 2i + j
(i) Construct A.
(ii) Find A + AT, A – AT
(iii) Express A as sum of a symmetric and skew-symmetric matrix. (May -2015)

Question 3.
(i) $$A=\left[\begin{array}{ll} 0 & 1 \\ 0 & 0 \end{array}\right], B=\left[\begin{array}{ll} 1 & 0 \\ 0 & 0 \end{array}\right]$$ then BA = _____
$$\begin{array}{l} \text { (a) }\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] & \text { (b) }\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right] \\ \text { (c) }\left[\begin{array}{ll} 0 & 1 \\ 0 & 0 \end{array}\right] & \text { (d) }\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right] \end{array}$$

(ii) Write $$A=\left[\begin{array}{cc} 3 & 5 \\ 1 & -1 \end{array}\right]$$ as the sum of a symmetric and a skew symmetric matrix.
(iii) Find the inverse of $$A=\left[\begin{array}{ll} 2 & -6 \\ 1 & -2 \end{array}\right]$$ (March 2016)

Question 4.
(i) If the matrix A is both symmetric and skew-symmetric, then A is a
(a) diagonal matrix
(b) zero matrix
(c) square matrix
(d) scalar matrix

(ii) If $$A=\left[\begin{array}{cc} 1 & 3 \\ -2 & 4 \end{array}\right]$$, then show that

(iii) Hence find A-1 (May 2016)
(iii) Using elementary transformations find the inverse of the matrix $$\left[\begin{array}{ll} 2 & 1 \\ 1 & 1 \end{array}\right]$$ (May 2017)