give an example of a 2 by 2 matrix and describe how to find the inverse of the matrix. when does a matrix not have an inverse?

There is a line with slope 1/a going through the point (a, a²). find the equation of the line perpendicular to this line at this point. (don’t let this problem intimidate you! solve the problem as you would if i’d given you specific values. just use variables instead.)

Evaluate the following expression 1/3^2

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).