4. Determine if the vector b is in the span of the columns of the matrix A, where [1 2 3 A = 7 8 10 11 12

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A: Given A is an m×n matrix whose columns are linearly independent. We have to find the nullity of A.

Q: Is the span of a matrix A is the same as the column space of A? T or F

A: We shall answer this question in next step

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A: Given that:

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A: The coefficient matrix is, Now,

Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

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A: Option B i.e 4

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A: …

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A: See the attachment

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A: Let matrix is A and the entries are aij .

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Q: 5. (a) Show that the columns of the matrix B below span R*. 1 1 0 2 1 3 0 3 0 2 3 3 0 0 6 5 В (3)…

A: See the attachment

Q: Consider the following matrix. A = [22 -2] How many vectors are in the basis of row(A)?

A: Given: Now,                   30-3222Reduced matrix to reduced row echelon form:=10-1012The rank of…

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Q: Consider the matrix A and the vectors p and q. 1 -3 9. A = -3 0 p= -6 | q = | -9 2 4

A:

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A: Detailed explanation mentioned below

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A: M = 0 will be the right answer.

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Q: Find all a and B> 0 so that the matrix 4 a 28 5 4 2 is strictly diagonally dominant.

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A: First we have to reduce into row echelon form of the given matrix.