MAT2611 ASSIGNMENT 4 2023
Problem 11
𝑣 = (3, 4,3)
𝑣1 = (3, 2, 1), 𝑣2 = (4, −2, 0), 𝑣3 = (1, 0, 0)
𝑣 = 𝑘1 𝑣1 + 𝑘2 𝑣2 + 𝑘3 𝑣3
(3, 4,3) = 𝑘1 (3, 2, 1) + 𝑘2 (4, −2, 0) + 𝑘3 (1, 0, 0)
(3, 4,3) = (3𝑘1 , 2𝑘1 , 1𝑘1 ) + (4𝑘2 , −2𝑘2 , 0) + (1𝑘3 , 0, 0)
(3, 4,3) = (3𝑘1 + 4𝑘2 + 𝑘3 , 2𝑘1 − 2𝑘2 , 𝑘1 )
3𝑘1 + 4𝑘2 + 𝑘3 = 3
2𝑘1 − 2𝑘2 = 4
𝑘1 = 3
2𝑘1 − 2𝑘2 = 4
2(3) − 2𝑘2 = 4
6 − 2𝑘2 = 4
−2𝑘2 = −2
𝑘2 = 1
3𝑘1 + 4𝑘2 + 𝑘3 = 3
3(3) + 4(1) + 𝑘3 = 3
9 + 4 + 𝑘3 = 3
𝑘3 = 3 − 13
𝑘3 = −10
𝑣 = 𝑘1 𝑣1 + 𝑘2 𝑣2 + 𝑘3 𝑣3
𝑣 = 3𝑣1 + 1𝑣2 − 10𝑣3
Coordinate vector is (3, 1, −10)
Problem 11
𝑣 = (3, 4,3)
𝑣1 = (3, 2, 1), 𝑣2 = (4, −2, 0), 𝑣3 = (1, 0, 0)
𝑣 = 𝑘1 𝑣1 + 𝑘2 𝑣2 + 𝑘3 𝑣3
(3, 4,3) = 𝑘1 (3, 2, 1) + 𝑘2 (4, −2, 0) + 𝑘3 (1, 0, 0)
(3, 4,3) = (3𝑘1 , 2𝑘1 , 1𝑘1 ) + (4𝑘2 , −2𝑘2 , 0) + (1𝑘3 , 0, 0)
(3, 4,3) = (3𝑘1 + 4𝑘2 + 𝑘3 , 2𝑘1 − 2𝑘2 , 𝑘1 )
3𝑘1 + 4𝑘2 + 𝑘3 = 3
2𝑘1 − 2𝑘2 = 4
𝑘1 = 3
2𝑘1 − 2𝑘2 = 4
2(3) − 2𝑘2 = 4
6 − 2𝑘2 = 4
−2𝑘2 = −2
𝑘2 = 1
3𝑘1 + 4𝑘2 + 𝑘3 = 3
3(3) + 4(1) + 𝑘3 = 3
9 + 4 + 𝑘3 = 3
𝑘3 = 3 − 13
𝑘3 = −10
𝑣 = 𝑘1 𝑣1 + 𝑘2 𝑣2 + 𝑘3 𝑣3
𝑣 = 3𝑣1 + 1𝑣2 − 10𝑣3
Coordinate vector is (3, 1, −10)