Question

11. (u x v) is orthogonal or perpendicular to the plane determined by vectors u and v. 12. Given the matrix A = [1 -2; 1 4], the vector x = [1; 1] is an eigenvector. 13. The points with coordinates A(0,0), B(1,2) and C(3,6) are collinear. 14. The distance between the vectors v1 = [1; -5] and v2 = [-3; -2] is 5. 15. The sum of the diagonal elements is equal to the sum of the eigenvalues of a square matrix.

          11. (u x v) is orthogonal or perpendicular to the plane determined by vectors u and v.
12. Given the matrix A = [1 -2; 1 4], the vector x = [1; 1] is an eigenvector.
13. The points with coordinates A(0,0), B(1,2) and C(3,6) are collinear.
14. The distance between the vectors v1 = [1; -5] and v2 = [-3; -2] is 5.
15. The sum of the diagonal elements is equal to the sum of the eigenvalues of a square matrix.

11. (u x v) is orthogonal or perpendicular to the plane determined by vectors u and v.
12. Given the matrix A = [1 -2; 1 4], the vector x = [1; 1] is an eigenvector.
13. The points with coordinates A(0,0), B(1,2) and C(3,6) are collinear.
14. The distance between the vectors v1 = [1; -5] and v2 = [-3; -2] is 5.
15. The sum of the diagonal elements is equal to the sum of the eigenvalues of a square matrix.

Added by Nuria M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/06/2023

Step 1

To check if (u x v) is orthogonal to the plane determined by vectors u and v, we need to check if the dot product of (u x v) with any vector in the plane is zero. Let w be any vector in the plane, then w = au + bv for some scalars a and b. Now, let's compute the Show more…

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11. (u !! v) is orthogonal or perpendicular to the plane determined by vectors u and v. 12. Given the matrix A = [1 -2; 1 4], the vector x = [1; 1] is an eigenvector. 13. The points with coordinates A(0,0), B(1,2) and C(3,6) are collinear. 14. The distance between the vectors v1 = [1; -5] and v2 = [-3; -2] is 5. 15. The sum of the diagonal elements is equal to the sum of the eigenvalues of a square matrix.