Let l: r^rightarrow r^3 be a transformation defined by l[(u_1, u_2, u_3, u_4)^t] = (u_1 + u_2, u_3 + u_4, u_1 + u_3)^t. [7 p] (a) show that l is a linear transformation. [9 b] (b) find a basis for kernel of l, ker(l), and determine its dimension. [9 p] (c) find a basis for image of r^4, l(r^4), and determine its dimension.

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b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: