IA_2019s2_tute2_sol - Mathematics IA Tutorial 2(week 3 Semester 2 2019 1 Solve the linear system x1 \u2212 x2 \u2212 x3 2x4 = 1 2x1 \u2212 2x2 \u2212 x3 3x4 = 3

# IA_2019s2_tute2_sol - Mathematics IA Tutorial 2(week 3...

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Mathematics IA Tutorial 2 (week 3) Semester 2, 2019 1. Solve the linear systemx1-x2-x3+ 2x4=12x1-2x2-x3+ 3x4=3-x1+x2-x3=-3by first bringing its augmented matrix into reduced row echelon form. 2. List all 2×2 matrices in reduced row echelon form. 1
3. Iff(x) = sinhx,xR, find the inverse function,f-1(x), giving youranswer in terms of the natural logarithm function.Hint:use the definition to writesinhxin terms of the exponentialfunction, and obtain a quadratic equation satisfied byex. 4. Find all solutions in [0, π] of the equation4 cos2x+ 3 sin2x-2 sinx= 2,giving your answers in exact form in terms of the arcsin function.Hint: Use one of the properties of thesinandcosfunctions to convertthe equation into a quadratic insinx. 2