span 0. Show that R-. 1 11. Show that R3 span 12. Show that R3 span In Exercises 13-16, describe the span of the given vectors (a) geometrically and (b) algebraically. 2 13. 3 14. 3 15. 2 2 16. 2 17. The general equation of the plane that contains the points (1, 0, 3), (-1, 1, -3), and the origin is of the form ax by +cz = 0. Solve for a, b, and c. 2 18. Prove that u, v, and w are all in span(u, v, w). 19. Prove that u, v, and w are all in span(u, u+ v, u + v+w) 20. (a) Prove that if u,.. , are vectors in R", S = u, u2,.. ., u}, and T = {u1, . . , U uk+1. . un n, then span(S) C span(T). [Hint: Rephrase this question in terms of linear combinations.] (b) Deduce that if R" = span(S), then R" = span ( T) 30 also. 31. 21. (a) Suppose that vector w is a linear combination of vectors u, . . , u and that each u, is a linear combination of vectors v, . . , V Prove that w is a linear combination of v,.. . , Vm and therefore span(u,,..., uk) span(vi,..,v,,) In E give

Q: 12 5 10

A:

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A:

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A: The given equation is: y=x+4

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A:

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A: simplified value is -24.44 v - 17.3

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A:

Q: Find the rank of A = ( 1   -1   2   3)                                       2  6  -8   1…

A: Rank of Matrix : It is the Number of Non Zero rows in reduced row echelon form.

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A: Given,    5y/10y    Cancelling y from both numerator and denominator to get,    5/10   Now, 5/10 can…

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A: To integrate.

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Q: Evaluate 5 (²) 4. dy -2

A: ∫-2-1 (y-2)dy/y ∫-2-1 (y - 2/y)dy [ 2y3/2/3 - 4y]-2-1 -2i/3 - 4i +42i +42i -14i/3 +82i

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A:

Q: 3 4 1 2 -2 -1 6 -3| Select one: а. 4 b. -40 C. 40 d. -4

A: Solve for the determinants

Q: In the

A: In the diagram it is given that, the angles <G and <H are complementary. m<G = 2x + 10…

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A: The expression is given by w+(-7) To evaluate: The value of the expression when w=-1.

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Q: 11 4.

A:

Q: 1) 6dx 3/3

A: ∫33361+x2dx=6∫33311+x2dx=6tan-1x333=6tan-13-tan-133=6tan-13-tan-113=6π3-π6=2π-π=π

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A: Topic:- integration

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A:

Q: 4 8 22

A: Given Triangle

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A:

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A:

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A: Given:   Two and two

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.