(a) Suppose a 3 by 5 matrix A has rankr= 3. Then the equation Ar b ( always / sometimes but not always) has ( a unique solution / many solutions/ no solution ). (b) What is the column space of A? Deseribe the nullspace of A.

Q: 20. The following are rules of transposition of a matrix except: (explain) a. (A")" = A b. (A + B)"…

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Q: -1 2 1 -2 and B = (-3 3 4 -2 2 2 -3 4 5. Find the quotient matrix A/B if A = 3 4 %3D -4 2 3 3/

A: The given matrices are: To find the quotient matrix A/B means, multiply matrix A with the inverse…

Q: What is the rank of the matrix?

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Q: What is the rank of the matrix A = 2 1 5 -1 2 -5 0 3? -3

A: See this solution in below.

Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

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Q: TRUE OR FALSE. The product of two m × n matrices is defined.

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Q: 1. Consider the matrices A₁ 4 = ( 1 ) - 1 3 0 A₂ 42 = (3-2) ₁ 4₁ = ( 2² -2²), , A3 0 -2 These…

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Q: Why does no 3 by 3 matrix have a nullspace that equals its column space?

A: To show why does no 3×3 matrix have a null space that equals its column space. We know the…

Q: How to get Linear equations from matrices ?

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Q: Q#2:-Find how many Even and Odd numbers inside the upper triangle of the secondary diagonal for…

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Q: 4 -3 1 34. The rank of the matrix A = -1 is 2 -7 -14 5 8 -1 (A) 1 (B) 2 (C) 3 (D) 0 (E) 4

A: Given Matrix is A=24-312-1-7-14548-1 we have to find the rank of matrix

Q: (v) 0 -1 0 1 0 0 ma ~ 0 ( 1 a -1 0 0 0 a 0 0 a 1 0 1 000

A: Given: A matrix .To find: The Row operations by which the matrix is reduced to

Q: (b) Let A be an m × n matrix. Prove that row(A)- = null(A). =

A: Given information: Matrix A is of order m×n. To prove: rowA⊥=nullA Orthogonal complement: Consider V…

Q: For Square Matrix A, B of the same size is it true (A + B)-1 = A-1 + B-l? Explain

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Q: Envision a 2 x 3 matrix.

A: Let A be the matrix with order 2×3, which represents 2 as number of rows and 3 as number of columns.

Q: What do 2 × 2 matrices represent graphically?

A: 2 × 2 matrices represent:

Q: Determine the real number values of the constant a with which the matrix A= (14 a1)  is positive…

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Q: 2 0 -1 1 -2 2 A = 2 -1 0 1 -1 6. ||

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Q: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

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Q: True or False The identity matrix has properties similar tothose of the real number 1.

A: We have to say that the given statement is true or false: The identity matrix has properties similar…

Q: for a matrix A 3 6 2 5 if f(x)=(x+2)(x-2), calculate f(A)

A: Given: Matrix A=3625 To Find: f(A) when f(x)=(x+2)(x-2)

Q: Give an example showing that the rank of the product of two matrices can be less than the rank of…

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Q: s this matrix in row-echelon form or reduced row-echelon form

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Q: How do I know if I can invert a matrix or not? What is a square matrix?

A: Ans(i):

Q: Give an example of a 3 × 3 matrix with real inputs that is not similar to a matrix diagonal

A: A matrix is said to be a diagonalisable  if it is similar to a diagonal matrix. Therefore we need to…