1. Find orthonormal bases, using the Gram-Schmidt process or otherwise, for the subspaces of R4 generated by the following sets of vectors. It is understood that the usual inner product in R4 is in use: («1, az , as , as), ) - È aß1. а. <1, 1, 1, 0>, <-1, 1, 2, 1>. b. (1, 1, 0, 0), <0, 1, 1, 0), (0, 0, 1, 1). <-1, 1, 1, 1>, <1, –1, 1, 1), <1, 1, – 1, 1).

Q: Sketch the points B = (-5, 0) and C= (-3, 3).

A: Given data: The first point given is B=(-5,0). The second point given is C=(-3, 3). The sketch of…

Q: 11) Endpoint: (6, –3), midpoint: (2, 6)

A:

Q: Write an equation to match the graph with coordinates (3,1), (2,2), (1,4), (0,8)

A: Solution of given equation is written in below steps.

Q: Find the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2, 2, -3).

A: Find the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2, 2, -3).

Q: Find the midpoint of the line segment from (4,-5) to (2,-1) Midpoint %3D

A: We have to find the midpoint of the line segment from (4,-5) to (2,-1) Formula Used -  The midpoint…

Q: The midpoint of a line segment MN is located at (-5,-8). The endpoint M is located at (3,4). What…

A:

Q: 7. Is the graph of x 6 vertical line or horizontal line? What is its slope?

A:

Q: what is the point and plot and Quadrant of (3,4)

A: Given that the point (3, 4)

Q: P.l-(-1.2) P.2-(3,-5) P1 P2 P1 P.1-(4,3) P.2-(-5,-2) Math-Aids.

A:

Q: Find the distance and midpoint of each pair of points (6,8) and (2,4) i. Distance ii. Midpoint…

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Q: Find the distance between the points. (8, 7), (0, 22).

A:

Q: name the quadrant or axis where each point lies (0,3) (-3,-3) (7,-2) (4,6)

A: We first need to locate all the points in the graph ÷

Q: Complete the equation of the line through (-1,6) and (7,-2). Use exact numbers. y=

A: We need to find the equation of the line through (-1,6) and (7,-2). The slope of the line passing…

Q: Find the midpoint of the line segment whose endpoints are (24,13) and (-30,-4).

A: Topic:-  geometry

Q: In the coordinate plane, a circle has center (2,-3) and passes through the point (5,0). What is the…

A:

Q: Write the equation of the line through (4, 9) and perpendicular to  y = 0.5x + 10. Please show…

A:

Q: Plot and then label the points A(0, - 3), B(3, - 4), C(5, 6), D(- 2, - 5), and E(- 3, 5).

A: Given the pouints are A(0,-3),B(3,-4),C(5,6),D(-2,-5) and E(-3,5).

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.