2. Find the values of x such that the rank of matrix 3x – 8 3 3 3 За — 8 3 - 3 3 3x – 8 is less than or equal to 2 Also find the rank for these values of r

Q: If A is an 7 x 12 matrix, then what is rank A² + dim nul (A²) equal to? Your

A: We can solve this as follows:

Q: • The Matrix B from 3 x 2 at by = 1- is 1. 3. 4. 1 -2

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Q: 1 Suppose that a 3 x 3 matrix A has det A = 1 and that its cofactor matrix is C = 1 2 |-7 4 2 Find…

A: Formula: Let A be a n×n matrix with non zero determinant then, A-1=1det ACT where C is the cofactor…

Q: Consider the following 3 x 3 matrix A and b in R, 1 -4 8 | A = 2 -3 2 1 5 -8 1

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Q: If matrix A is 12 xc and matrix K is 4 x t, their product AK is r x 7, what are the values of c, t,…

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Q: Consider the following linear equations : -8x + 4y + 3z = -4 -8x + (18 – k)y+ 2z = -2 --8x + 4y + (7…

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Q: What is a, if A = 2 4 is a singular matrix ? a Simplify (1+x)(1+x²)(1 – x + x?) in descending order…

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Q: The matrix is not invertible for what value of x 2 1 1 1 31

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Q: If C is a matrix of 6 x 6 and the matrix equation C x = v is consistent for every v in R®, is it…

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Q: 4. Suppose A is an m x n matrix with the property that for all b in R™ the equation Ax = b has at…

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Q: 4 2 If A is a non-singular matrix whose inverse is find A. 1 - 2 -1] -1] 1 В. -1 1/2 С. -1/2 1 D. |…

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Q: (4) Given a matrix X of independent variables, psudo-inverse X† is defined as (X"X)-'x" (a) If X is…

A: If a matrix is of order (mXn) then transpose of A is of order (nXm).

Q: 5. Suppose that A is a 3 x 5 matrix, and the rows of A are linearly independent. What is the…

A: A is a 3x5 matrix. And rows of A are linearly independent. So that dimension of range space of Ax…

Q: Suppose that A is a 4 x 4 matrix with det(A) = 5. Then + (24–1) - [2 Enter your answer exactly, as a…

A: We have to find determinant

Q: 9. . Suppose that A = PDP¯' and B = 31 + 2A + A². 5 Let D a Find a diagonal matrix D1 such that B =…

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Q: Given. Q(x)=3x² + x} +8x? –2x,x, –4.x,x3 Q(x)=x" Ax wher A is symmetric matrix 1 a, = a, = 3…

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Q: [1 1 1] L3 -2 3 1[k [k 1 1 -2||1 = 14 1

A: Given,           k11·10301-23-21·k11=14To find : The value of k that satisfies the following matrix…

Q: Let A be an n xn matrix. The linear system AX = 4X has a unique solution if and only if, А. А - 4ln…

A:

Q: Suppose A is an m x n matrix with the property that for all b in R" the equation Ax = b has at most…

A: Given: A is an m x n matrix with the property that for all b in Rm the equation Ax = b has at most…

Q: If A is a 3 x3 matrix and det(A) =-3, what is det(4A)?

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Q: If the order of matrix is m x p. And the order of B is p xn Then the order of matrix AB is O nxp O m…

A: Here I am attaching image so that you understand each and every step.

Q: Show that if C and D are n×n row equivalent matrices, and Cx=0 has a non-trivial solution x !=0,…

A: Given that C and D are row equivalent matrices such that the system Cx=0 has a non trivial solution…

Q: Are there values of r and s for which [ 1 0 r- 2 0 s- 4 r+2 | 3 has rank 1 or 2? If so, find those…

A: Let's find.

Q: Give the size of the following matrix 1. 1 1 1 5 2X2 1X3 B 3X3 2X3 2X1 D 3X2 H. Otherwise

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Q: If you multiply this elementary matrix: [1 0 0 0] 0 1 0 0 0 0 1 0 E 0 0 0 2 by A to form EA, it has…

A:

Q: The order of the single matrix obtained from 1 1 -1 To 1 23 is 1 0 21 -1 0 2 2 0 3 2 (a) 2 x 3

A: Here the order of the matrix needs to find out for both terms. Subtraction and addition won't affect…

Q: 2. Find the values of k for which the matrix B is invertible. -2 B= 0 k 1 3 2 1 4 -1

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Q: Give an example of a matrix A such that (1) Ax=b has a solution for infinitely many b ∈ R3 but (2)…

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Q: Given 4x6 matrix A with rank(A)s 3, the nullity n of A must be a. 4<n<6 b. none of these c. 1<n<3 O…

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Q: If the matrix A is m x n and A = b is solvable for every b then O a. C(A) = Rm O b. m > n O c. C (A)…

A: For first question: Option (a) is correct. C(A) = R^m.

Q: 3. Show that for any n x n matrix A of rank r, we have ||4|| < ||4||ES VFl|4||.

A: To show that: A≤AF≤ rA  for any n×n matrix A of rank r.

Q: Suppose that 2 3 Solve the linear system Ax = b for each of the following matrices b: 8 (b) 15 (a)

A: Given: A-1=1213 (a) Ax=bx=A-1b Substitute the respective values. x=121346=4+124+18=1622 Therefore,…

Q: Find the values of k for which the matrix B is invertible. B = -2 1 0 2 k 4 3 1

A: We need to determine the values of k for which the matrix: B is invertible.

Q: 5. Use the matrices to solve the x-2y+3z = 4 system: 3x- 4y+z = 4 2x +3y-4z = -2

A: We have to solve the equation by matrix method.

Q: Give an example of a matrix A such that (1) Ax = b has a solution for infinitely many b e R°, but…

A: If  the dimension of the column space of  A will be 3  (or if A has set of three linearly…

Q: 4 2 If A is a non-singular matrix whose inverse is 1 1 find A. - 2 -1 1 D. -1 1/2 1 В. С. -1/2 2 А.…

A: Goal is to find inverse of matrix 4211

Q: 1. Suppose (B – C) D = 0, where B and C are m x n matrix and D is invertible. Show B = C

A: ( B - C )D = 0 where B and C are m × n matrix and D is invertible.  Then, we have to prove that B =…

Q: If 4 [a] is a 3x3 matrix, such that ay i (2m-j) then the diagonal elements are

A:

Q: 13. Suppose that a 3 × 3 matrix A factors into a product 1 0 1 Determine the value of det(A).

A: It is known that for n×n matrices A and B detAB=detAdetB                      (i) Given…

Q: determine of matrix 2x 3x e e 2e 3x 2x 3e Select one: 5x a. 2e 5x b. 1/5 e 5x С. 5e 5x d. e

A: Determine of matrix   a   b  c   d is given as    = a*d-b*c

Q: Suppose that A is a 3×3 matrix and det (A) = -4. What is det (4A)?

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: If A is m x n matrix has rank of 5 and the dimension of N(AT) is 2 and dimension of N(A) is 4 then:…

A: We have to find value of n.

Q: Are there values of r and s for which 1 0 r- 4 4 0 s- 2 r + 4 5 has rank 1 or 2? If so, find those…

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Q: Determine the dimensions of the given matrix G -3 15 0 G = 0. 3 3 1 -1 6 O 3 X 4 O 4 X 3 4X4 12 X 0

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Q: 4. The adjoint of the matrix A=1 2 0 3 1 is b. -1 10 0 -15 -2 4 -1 -1 -5 -2 d. Sone of these c. -1

A: A=20-1120311 first, we need to find the minor matrix M1, 1=det2011:  2 M1, 2=det1031:  1 M=1,…

Q: Consider the two matrices: 2 4 1 B= -5 A= -3 Compute A+ 3B. The result is equal to:

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Q: Suppose B and D are the following two bases for P2: B=|4x²-4x-2, ²-4x−2, 3x²-x, −3x−3] D= [-3x−3,…

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Q: For which value of k is the following matrix NOT invertible? [1 2 3 1 A = 0 -3 -4 5 -4 k 1 -1 7 3 1…

A: The given problem is to find the value of k for which the given matrix is not invertible.

Q: 1. Use matrix inversion to solve for x, y, and z if: x + 2y + 2z = −1 y − x − z = 0 2z + 3y + 3x = 1

A: see below the answer

Q: Which of the following augmented matrices corresponds to the system giver 3x + y – 9z = 0 -8x – 2y –…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.