4. State with a brief explanation whether the following statements are true or false. (a) The vectors (1,0) and (0, 1) span R². (b) The vectors (2,−1), (0, 1), and (1,0) span R². (c) The vectors (1,0) and (0, 1) are linearly independent. (d) The vectors (2, -1), (0, 1) and (1,0) are linearly independent. (e) A set of any two vectors in R² is a basis for R². (f) A set of any three vectors in R² must be linearly dependent. (g) R2 is a subspace of R³.

Q: = (4, 1, a), Q = (–2, 0, b) and v = i – 3j + 4k be two points and a vector in R³ respectively. (a)…

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Q: Determine nonzero vectors that are orthogonal to the following vectors. (a) (1, 5)     (b) (6, −1)…

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Q: The plane passing through the three points A(4, –3, –4), B(-4, –3,2) and C(-3,3, –2) can be…

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Q: Let a = (6, −3, −5) and b = (7, -2, 10) be vectors. (A) Find the scalar projection of b onto a.…

A: Let  be vectors.(A) To find the scalar projection of .(B) To decompose the vector  into a component…

Q: X = Find the vector equation for the line of intersection of the planes x − 5y + 5z = −5 and x + 5z…

A: Given the equation of planes x-5y+5z=-5 and x+5z=1. To find the vector equation for the line of…

Q: Point P₁ lies on the line {₁:[4,4,-3]+t[2,1,−1],tER, and point P2 lies on the line…

A: Solution : Given that the lines l1 : 4,4,-3+t2,1,-1l2 : -2,-7,2+s3,2,-3

Q: Find the cross products u xv and vxu for the vectors u = = (3,5,0) and v = (0,3, - 6). uxv = (Di+…

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Q: X = Find the vector equation for the line of intersection of the planes x - 5y + 5z = −5 and x + 5z…

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Q: Equation of the plane passes through the point (1, 2, 3) and parallel to the vector A= 2i+3j :+k and…

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Q: - 3)² = 81 then, find its ce or a=<3, -1

A: 1. Given: The points are 2,3,-6 and -1, 4, 5 To find the distance between the given points. The…

Q: The plane passing through the three points A(0, 1,3), B(3,4,3) and C(2,3, –1) can be expressed as a…

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