The three solutions of the equation f(x) = 0 are -2, 0, and 3. Therefore, the three solutions of the equation f(x - 2) = 0 are?
f(x-2) becomes zero when (x-2) equals -2, 0, 3 so, x-2= -2 x=0 or x-2=0 x=2 or x-2= 3 x= 5 Thus the solutions of f(x-2)=0 are 0,2,5
Linear Algebra: Why does sum of variance of columns in a matrix stay constant during rotations and intuitively why is useful for ANOVA, dimensional reduction, etc?
A rotation matrix R has the property that RTR=I. Rotating a matrix X consists of computing the product RX. When you left-multiply this new matrix by its transpose, the rotation matrices disappear, and you're left with the original product XTX. There is some statistical content to a similar observation in factor analysis, where rotation matrices are used to find interpretable coefficients.