Matrix Operations addition and subtraction

Matrix Operations: Addition and Subtraction

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Solve the following practice questions based on Addition and Subtraction of Matrix Operations:

Q1. Given A = [3−124], B = [52−31], find A + B and A – B.

Solution:

A + B = [3+5−1+22+(−3)4+1] = [81−15]

A – B = [3−5−1−22−(−3)4−1] = [−2−353]

Q2. If A = [123456], B = [−1023−51], find 2A + B.

Solution:

2A = [24681012]

2A + B = [2+(−1)4+06+28+310+(−5)12+1] = [14811513]

Q3. Given A = [70−25], B = [341−5], C = [2−103], find A + B – C.

Solution:

A + B = [104−10]

A + B – C = [10−24−(−1)−1−00−3] = [85−1−3]

Q4. If A + B = [5739] and A = [2314], find matrix B.

Solution:

B = (A + B) – A

B = [5−27−33−19−4] = [3425]

Q5. Given, A = [1234], B = [5678], Find A+B.

Solution:

A + B = [1+52+63+74+8] = [681012]

Q6. Given A = [0−1234−5], B = [123−105], Find A + B.

Solution:

A + B = [0+1−1+22+33+(−1)4+0−5+5] = [115240]

Q7.  Given A = [1001], B = [2345] and C = [−1−2−3−4], Find A + B + C.

Solution:

A + B = [3346]

A + B + C = [3+(−1)3+(−2)4+(−3)6+(−4)] = [2112]

Q8. Given A = [1.52.53.54.5], B = [0.51.52.53.5], Find A+B.

Solution:

A + B = [1.5+0.52.5+1.53.5+2.54.5+3.5] = [2468]

Q9. If A + B = [78910] and A = [3456], find B.

Solution:

B = (A + B) − A
B = [7−38−49−510−6] = [4444]

Q10. Given A = [9876], B = [1234], Find A – B.

Solution:

A − B = [9−18−27−36−4] = [8642]

Q11. Given A = [5−3204−1], B = [21−34−26], Find A – B.

Solution:

A − B = [5−2−3−12−(−3)0−44−(−2)−1−6] = [3−45−46−7]

Q12. Given A = [10101010], B = [3456] and C = [2101], Find A – B – C.

Solution:

A − B = [7654]

A − B − C = [7−26−15−04−1] = [5553]

Q13. If A − B = [2345] and A = [6789], find B.

Solution:

B = A − (A − B)
B = [6−27−38−49−5] = [4444]

Q14. Given A = [4213], B = [1122], Find 2A − 3B.

Solution:

2A = [8426]
3B = [3366]
2A − 3B = [8−34−32−66−6] = [51−40]

Q15. If A = [3−214], find 5A.

Solution:

5A = [5×35×(−2)5×15×4] = [15−10520]

Q16. Given B = [20−1352], compute -3B.

Solution:

-3B = [−603−9−15−6]

Q17. If A = [69−123], find 13​A.

Solution:

13​A = [23−41]

Q18. If A = [1234], find 4A – 2A.

Solution:

4A – 2A = 2A

2A = [2468]

Q19. If A = [1234], Find 4A.

Solution:

4A = [4×14×24×34×4] = [481216]

Q20. If A = [2−105], Find −3A .

Solution:

−3A = [−3×2−3×(−1)−3×0−3×5] = [−630−15]

Q21. If A = [8642], Find 12​A.

Solution:

 12​A = [4321]

Q22. If A = [1001], Find 2A + 3A.

Solution:

2A + 3A = 5A = [5005]

Q23. If 5A = [15253545], find A.

Solution:

A = 15​ × 5A = [15÷525÷535÷545÷5] = [3579]

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