Tamil Nadu Board Solutions for Chapter: Algebra, Exercise 34: Exercise 3.2

The number of points of intersection of the quadratic polynomial $x^2+4x+4$ with the $x$-axis is

For the given matrix $\mathrm{A}=\left(\begin{array}{rrrr}1& 3& 5& 7\\ 2& 4& 6& 8\\ 9& 11& 13& 15\end{array}\right)$ the order of the matrix $A^T$ is

If $A$ is a $2\times 3$ matrix and $B$ is a $3\times 4$ matrix, how many columns does $AB$ have

If number of columns and rows are not equal in a matrix then it is said to be a

Transpose of a column matrix is a

Find the matrix $X$, if $2X+\left(\begin{array}{ll}1& 3\\ 5& 7\end{array}\right)=\left(\begin{array}{ll}5& 7\\ 9& 5\end{array}\right)$.

If $A=\left(\begin{array}{ll}1& 2\\ 3& 4\\ 5& 6\end{array}\right) \text{and} B=\left(\begin{array}{lll}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right)$, then we can calculate

If $A=\left(\begin{array}{lll}1& 2& 3\\ 3& 2& 1\end{array}\right), B=\left[\begin{array}{rr}1& 0\\ 2& -1\\ 0& 2\end{array}\right]$ and $C=\left(\begin{array}{rr}0& 1\\ -2& 5\end{array}\right)$, then $\text{ (i) }AB+C=\left(\begin{array}{ll}5& 5\\ 5& 5\end{array}\right)$,$\text{ (ii) }BC=\left(\begin{array}{rr}0& 1\\ 2& -3\\ -4& 10\end{array}\right)$,$\text{ (iii) }BA+C=\left(\begin{array}{ll}2& 5\\ 3& 0\end{array}\right)$,$\left(\mathrm{iv}\right) \left(AB\right)C=\left(\begin{array}{ll}-8& 20\\ -8& 13\end{array}\right)$.

The correct statements among the given are