If $\left(\begin{array}{l l }2x+1 & 2y \\ 0 & y²+1\end{array}\right)$ = $\left(\begin{array}{l l }x+3 & 10 \\ 0 & 26\end{array}\right)$ , write the value of (x + y).

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ denote the position vectors of points A and B respectively and C is a point on AB such that AC = 2 CB, then write the position vector of C.

If 3A – B = $\left(\begin{array}{l l }5 & 0 \\ 1 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l }4 & 3 \\ 2 & 5\end{array}\right)$ , then find the matrix A.

If A = $\left(\begin{array}{l l }3 & 10 \\ 2 & 7\end{array}\right)$ , then write A⁻¹.

If A is a 3 × 3 matrix, whose elements are given by $a_{i j}={\frac{1}{3}}|-3i+j\,|$ , then write the value of $a_{23}$.

If A is a square matrix of order 3 such that $|a d j\,A|$ = 225, find $|A^{\prime}|.$

If A is a square matrix such that A² = A, then write the value of (I + A)² – 3A.

If a line has direction ratios 2, – 1, – 2, then what are its direction cosines ?

If a unit vector $\stackrel{\rightarrow}{a}\$ makes an angle $\frac{\pi}{3}$ with $\stackrel{\wedge}{i},$ $\frac{\pi}{4}$ with $\stackrel{\wedge}{j}$ and an acute angle θ with $\stackrel{\wedge}{k}$, then find the value of θ.

If the determinant of matrix A of order 3 × 3 is of value 4, write the value of |3A|.

Is A is square matrix of order 3 and |2A| = k|A|, then find the value of k.

L and M are two points with position vectors $2\stackrel{\rightarrow}{a}-\stackrel{\rightarrow}{b}$ and $\stackrel{\rightarrow}{a}+2\stackrel{\rightarrow}{b}$ respectively. Write the position vectors of a point N which divides the line segment LM in the ratio 2:1 externally.

P and Q are two points with position vectors $3\stackrel{\rightarrow}{a}-2\stackrel{\rightarrow}{b}$ and $\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}$ respectively. Write the position vector of a point R which divides the line segment PQ externally in the ratio 2 : 1.

The value of the determinant of a matrix A of order 3 × 3 is 4. Find the value of |5A|.

Write the inverse of the matrix $\left(\begin{array}{l l }cosθ & -sinθ \\ sinθ & cosθ\end{array}\right)$ .