Section 3.3

  1. 1.

    1. (a) F

    2. (b) F

    3. (c) T

    4. (d) F

    5. (e) F

    6. (f) F

    7. (g) T

    8. (h) F

  2. 2.

    1. (a) {(−31)}

    2. (c) {(−111)}

    3. (e) {(−2100),(3010),(−1001)}

    4. (g) {(−3110),(1−101)}

  3. 3.

    1. (a) {(50)+t(−31): t∈R}

    2. (c) {(211)+t(−111): t∈R}

    3. (e) {(1000)+r(−2100)+s(3010)+t(−1001): r,s,t∈R}

    4. (g) {(0001)+r(−3110)+s(1−101): r,s∈R}

  4. 4.

    1. (b)

      1. (1) A−1=(130131913−29−4923−19)

      2. (2) (x1x2x3)=(30−2)

  5. 6. T−1{(1,11)}={(112−920)+t(1−12): t∈R}

  6. 7. The systems in parts (b), (c), and (d) have solutions.

  7. 11. The farmer, tailor, and carpenter must have incomes in the proportions 4 : 3 : 4.

  8. 13. There must be 7.8 units of the first commodity and 9.5 units of the second.

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