Question

Evaluate $\textstyle\int\!{\frac{x^{3}-x^{2}+x-1}{x-1}}\,d x\,.$

Let A and B are matrices of order 3 x 2 and 2 x 4 respectively. Write the order of matrix (AB).

Let A = $A\ =\ {\left(\begin{array}{l l}{2}&{-1}\\ {3}&{4}\end{array}\right)}$ , B = $A\ =\ {\left(\begin{array}{l l}{5}&{2}\\ {7}&{4}\end{array}\right)}$ , C = $A\ =\ {\left(\begin{array}{l l}{2}&{5}\\ {3}&{8}\end{array}\right)}$ , find a matrix D such that CD - AB = 0.

Write the degree of the differential equation : $\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-2{\frac{d^{2}y}{d x^{2}}}-{\frac{d y}{d x}}+1=0.$

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

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.

Write the order of the differential equation: $\log\,\left(\frac{d^{2}y}{d x^{2}}\right)=\left(\frac{d y}{d x}\right)^{3}+x$