Ask Question
21 October, 00:52

Find the inverse of the following matrix without using a calculator 1-1 2 - 3 2 1 0 4 - 25

+2
Answers (1)
  1. 21 October, 01:07
    0
    18 - (17/3) (5/3)

    25 (25/3) (7/3)

    4 (4/3) (1/3)

    Step-by-step explanation:

    You can solve this problem by using the Gauss-Jordan method.

    You have the original matrix and then the Identity matrix.

    So:

    Original Identity

    1 - 1 2 1 0 0

    -3 2 1 0 1 0

    0 4 - 25 0 0 1

    By the Gauss-Jordan method, in the original place you will have the identity and in the place that the identity currently is you will have the inverse matrix:

    So, let's start by setting the first row element to 0 in the second and the third line.

    The first row element of the third line is already at zero, so no changes there. In the second line, we need to do:

    L2 = L2 + 3L1

    So now we have the following matrixes.

    1 - 1 2 | 1 0 0

    0 - 1 7 | 3 1 0

    0 4 - 25 | 0 0 1

    Now we need the element in the second line, second row to be 1. So we do:

    L2 = - L2

    1 - 1 2 | 1 0 0

    0 1 - 7 | - 3 - 1 0

    0 4 - 25 | 0 0 1

    Now, in the second row, we need to make the elements at the first and third line being zero. So, we have the following operations:

    L1 = L1 + L2

    L3 = L3 - 4L2

    Now our matrixes are:

    1 0 - 5 | - 2 - 1 0

    0 1 - 7 | - 3 - 1 0

    0 0 3 | 12 4 1

    Now we need the element in the third line, third row being one. So we do:

    L3 = - L3

    1 0 - 5 | - 2 - 1 0

    0 1 - 7 | - 3 - 1 0

    0 0 1 | 4 (4/3) (1/3)

    Now, in the third row, we need the elements in the first and second line being zero. So we do:

    L1 = L1 + 5L3

    L2 = L2 + 7L3

    So we have:

    1 0 0 | 18 - (17/3) (5/3)

    0 1 0 | 25 (25/3) (7/3)

    0 0 1 | 4 (4/3) (1/3)

    So the inverse matrix is:

    18 - (17/3) (5/3)

    25 (25/3) (7/3)

    4 (4/3) (1/3)
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Find the inverse of the following matrix without using a calculator 1-1 2 - 3 2 1 0 4 - 25 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers