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2.1.1: Exercises 2.1 - Mathematics


Matrices (A) and (B) are given below. In Exercises (PageIndex{1}) - (PageIndex{6}), simplify the given expression.

[A=left[egin{array}{cc}{1}&{-1}{7}&{4}end{array} ight]qquad B=left[egin{array}{cc}{-3}&{2}{5}&{9}end{array} ight] onumber]

Exercise (PageIndex{1})

(A+B)

Answer

(left[egin{array}{cc}{-2}&{-1}{12}&{13}end{array} ight])

Exercise (PageIndex{2})

(2A-3B)

Answer

(left[egin{array}{cc}{11}&{-8}{-1}&{-19}end{array} ight])

Exercise (PageIndex{3})

(3A-A)

Answer

(left[egin{array}{cc}{2}&{-2}{14}&{8}end{array} ight])

Exercise (PageIndex{4})

(4B-2A)

Answer

(left[egin{array}{c}{-14}{-5}{-9}end{array} ight])

Exercise (PageIndex{5})

(3(A-B)+B)

Answer

(left[egin{array}{cc}{9}&{-7}{11}&{-6}end{array} ight])

Exercise (PageIndex{6})

(2(A-B)-(A-3B))

Answer

(left[egin{array}{cc}{-2}&{1}{12}&{13}end{array} ight])

Matrices (A) and (B) are given below. In Exercises (PageIndex{7}) - (PageIndex{10}), simplify the given expression.

[A=left[egin{array}{c}{3}{5}end{array} ight]qquad B=left[egin{array}{c}{-2}{4}end{array} ight] onumber]

Exercise (PageIndex{7})

(4B-2A)

Answer

(left[egin{array}{c}{-14}{6}end{array} ight])

Exercise (PageIndex{8})

(-2A+3A)

Answer

(left[egin{array}{c}{-12}{2}end{array} ight])

Exercise (PageIndex{9})

(-2A-3A)

Answer

(left[egin{array}{c}{-15}{-25}end{array} ight])

Exercise (PageIndex{10})

(-B+3B-2B)

Answer

(left[egin{array}{c}{0}{0}end{array} ight])

Matrices (A) and (B) are given below. In Exercises (PageIndex{11}) - (PageIndex{14}), find (X) that satisfies the equation.

[A=left[egin{array}{cc}{3}&{-1}{2}&{5}end{array} ight]qquad B=left[egin{array}{cc}{1}&{7}{3}&{-4}end{array} ight] onumber]

Exercise (PageIndex{11})

(2A+X=B)

Answer

(X=left[egin{array}{cc}{-5}&{9}{-1}&{-14}end{array} ight])

Exercise (PageIndex{12})

(A-X=3B)

Answer

(X=left[egin{array}{cc}{0}&{-22}{-7}&{17}end{array} ight])

Exercise (PageIndex{13})

(3A+2X=-1B)

Answer

(X=left[egin{array}{cc}{-5}&{-2}{-9/2}&{-19/2}end{array} ight])

Exercise (PageIndex{14})

(A-frac{1}{2}X=-B)

Answer

(X=left[egin{array}{cc}{8}&{12}{10}&{2}end{array} ight])

In Exercises (PageIndex{15}) - (PageIndex{21}), find values for the scalars (a) and (b) that satisfy the given equation.

Exercise (PageIndex{15})

(aleft[egin{array}{c}{1}{2}end{array} ight]+bleft[egin{array}{c}{-1}{5}end{array} ight]=left[egin{array}{c}{1}{9}end{array} ight])

Answer

(a = 2), (b = 1)

Exercise (PageIndex{16})

(aleft[egin{array}{c}{-3}{1}end{array} ight]+bleft[egin{array}{c}{8}{4}end{array} ight]=left[egin{array}{c}{7}{1}end{array} ight])

Answer

(a = -1), (b = 1/2)

Exercise (PageIndex{17})

(aleft[egin{array}{c}{4}{-2}end{array} ight]+bleft[egin{array}{c}{-6}{3}end{array} ight]=left[egin{array}{c}{10}{-5}end{array} ight])

Answer

(a = 5/2 + 3/2b)

Exercise (PageIndex{18})

(aleft[egin{array}{c}{1}{1}end{array} ight]+bleft[egin{array}{c}{-1}{3}end{array} ight]=left[egin{array}{c}{5}{5}end{array} ight])

Answer

(a = 5), (b = 0)

Exercise (PageIndex{19})

(aleft[egin{array}{c}{1}{3}end{array} ight]+bleft[egin{array}{c}{-3}{-9}end{array} ight]=left[egin{array}{c}{4}{-12}end{array} ight])

Answer

No solution.

Exercise (PageIndex{20})

(aleft[egin{array}{c}{1}{2}{3}end{array} ight]+bleft[egin{array}{c}{1}{1}{2}end{array} ight]=left[egin{array}{c}{0}{-1}{-1}end{array} ight])

Answer

(a=-1), (b=1)

Exercise (PageIndex{21})

(aleft[egin{array}{c}{1}{0}{1}end{array} ight]+bleft[egin{array}{c}{5}{1}{2}end{array} ight]=left[egin{array}{c}{3}{4}{7}end{array} ight])

Answer

No solution.


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