IITM BS Question 27 - Week 7 Practice

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IITM BS Question 27 - Week 7 Practice | Prasnya

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Q27Numerical2 Marks30 Apr 2023

Let V1, V2 and V3 represent the subspaces {

(x,y,z)

| 2x + 3y + 4z = 0 }, {

(x,y,z)

| x + 2y + z = 0 } and {

(x,y,z)

| x + y + 2z = 0 }, respectively of

\mathbb{R}^3

. Let Ai (i = 1, 2, 3) be the affine spaces corresponding to Vi. Suppose A1 contains

(1, 1, -2)

, A2 contains

(-2, 1, 1)

and A3 contains

(1, -2, 1)

. If (x1, x2, x3) is the point of intersection of A1, A2 and A3, find x1 + 2x2 + x3.

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Q27

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30 Apr 2023

Mathematics 2 · Week 7

Q27.Let V1, V2 and V3 represent the subspaces {

(x,y,z)

| 2x + 3y + 4z = 0 }, {

(x,y,z)

| x + 2y + z = 0 } and {

(x,y,z)

| x + y + 2z = 0 }, respectively of

\mathbb{R}^3

. Let Ai (i = 1, 2, 3) be the affine spaces corresponding to Vi. Suppose A1 contains

(1, 1, -2)

, A2 contains

(-2, 1, 1)

and A3 contains

(1, -2, 1)

. If (x1, x2, x3) is the point of intersection of A1, A2 and A3, find x1 + 2x2 + x3.

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