Which of the following matrices is not invertible? (A) [3 2 6 4] (B) [7 2 7 3] (

Question

Which of the following matrices is not invertible? (A) [3 2 6 4] (B) [7 2 7 3] (C) [9 4 0 4] (D) [9 6 3 5 ] Which of the following matrices is not an elementary matrix? (A) [1 5 0 1] (B) [1 0 1 2] (C) [0 1 0 1 0 0 0 0 1] (D) [1 0 0 0-2 0 0 0 1] For which elementary matrix E will the equation EA = B hold? A = [1 0 2 4 0 10 6 1 9], B = [1 0 0 4 0 2 6 1 -3] (A) [1 0 2 0 1 0 0 0 1] (B) [1 0 0 0 0 1 0 1 0] (C) [1 0 -2 0 1 0 0 0 1] (D) [0 0 1 0 1 0 1 0 0] Which matrix will be used as the inverted coefficient matrix when solving the following system? 3x_1 + x_2 = 4 5x_1 + 2x_2 = 7 (A) [2 -5 -1 3] (B) [-2 5 1 -3] (C) [2 5 1 3] (D) [-2 -5 -1 -3] What value of b makes the following system consistent? 4x_1 + 2x_2 = b 2x_1 + x_2 = 0 (A) b = -1 (B) b = 0 (C) b = 1 (D) b = 2

Explanation / Answer

8)

The matrices are non invertible if the determinant is ZERO

a)
Det = 3(4) - 2(6)
= 12 - 12
= 0
Since Det = 0, this is non invertible

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8b)
Det = 7(3) - 2(7)
Det = 21 - 14
Det = 7 --> nonzero
So, yes, it is invertible

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8c)
Det = 9(4) - 0(4)
36 - 0
36
Nonzero
So, invertible

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8d)
Det = 9(5) - 6(3)
45 - 18
27
Nonzero
So, invertible

So, for 8, option A is the answer

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9)
In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation.

In option A, we can do R2 ---> R2- 5R1 anmd we get the identity matrix.
So, not option A

in option D, we can do R2 ---> R2 / -2
to get the identity matrix
So, not option D

in option C, we can do an interchange of R2 and R1 and
we get identity I

So option B is the answer

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10)
option C

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11)
Coefficient matrix is
first row = [3 1]
second row = [5 2]

Inverted matrix is obtained by switching the main diagonal elements
2 and 3. And also, switching the signs of the other two elements, 1 and 5.

[2 -1]
[-5 3]

Option A

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12)
Notice that the first can be written as:
2(2x1 + x2) = b
2x1 + x2 = b/2
For it to be consistent with the second equation,
since they have same Left Hand side,
we can do :

b/2 = 0

b = 0

option B

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