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Starting with the square matrix A, create the augmented matrix AI = [A:I] which represents the columns of A followed by the columns of I, the identity matrix.
Using elementary row operations only (no column operations), convert the left half of the matrix to the identity matrix. The right half, which started off as I, will now be the inverse of A.
Starting with the square matrix A, create the augmented matrix AI = [A:I] which represents the columns of A followed by the columns of I, the identity matrix.
Using elementary row operations only (no column operations), convert the left half of the matrix to the identity matrix. The right half, which started off as I, will now be the inverse of A.
Starting with the square matrix A, create the augmented matrix AI = [A:I] which represents the columns of A followed by the columns of I, the identity matrix.
Using elementary row operations only (no column operations), convert the left half of the matrix to the identity matrix. The right half, which started off as I, will now be the inverse of A.
Starting with the square matrix A, create the augmented matrix AI = [A:I] which represents the columns of A followed by the columns of I, the identity matrix.
Using elementary row operations only (no column operations), convert the left half of the matrix to the identity matrix. The right half, which started off as I, will now be the inverse of A.
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SteveStarting with the square matrix A, create the augmented matrix AI = [A:I] which represents the columns of A followed by the columns of I, the identity matrix.
Using elementary row operations only (no column operations), convert the left half of the matrix to the identity matrix. The right half, which started off as I, will now be the inverse of A.
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How do you find the inverse of a 10x2 matrix?
A non-square matrix cannot be inverted.
What is an orthogonal matrix?
A matrix A is orthogonal if itstranspose is equal to it inverse. So AT is the transpose of A and A-1 is the inverse. We have AT=A-1 So we have : AAT= I, the identity matrix Since it is MUCH easier to find a transpose than an inverse, these matrices are easy to compute with. Furthermore, rotation matrices are orthogonal. The inverse of an orthogonal matrix is also orthogonal which can be easily proved directly from the definition.
How do you find the inverse of A in system of linear equation and matrices?
First, we need to recall that a linear equation does not involve any products or roots of variables. All variables occur only to the first power and do not appear as arguments for trigonometric, logarithmic, or exponential functions. For example, x + √y = 4, y = sin x, and 2x + y - z + yz = 5 are not linear.To solve a system of equations such as3x + y = 52x - y = 3all information required for the solution is emboded in the augmented matrix (imagine that I put those information into a rectangular arrays)3 1 52 -1 3and that the solution can be obtained by performing appropriate operations on this matrix.The matrix of this system linear equations is a square matrix A such as3 12 -1Think this matrix asa bc dTo find an inverse of this square matrix A (2 x 2), we need to find a matrix B of the same size such that AB = I and BA = I, then A is said to be invertible and B is called the inverse of A. If no such a matrix can be found, then A is said to be singular.An invertible matrix has exactly one inverse.A square matrix A is invertible if ad - bc ≠ 0 (where ad - bc is the determinant)The formula of finding the inverse of a square matrix A isA-1 = [1/(ad - bc)][d -b the second row -c a](I'm sorry, I can't draw the arrays)So let's find the inverse of our example.A-1 = [1/(-3 -2)][-1 -1 the second row -2 3] = [-1/-5 -1/-5 the sec. row -2/-5 3/-5] =1/5 1/52/5 -3/5A n x m matrix cannot have an inverse. A n x n matrix may or may not have an inverse.To find the inverse of a n x n matrix we should to adjoin the identity matrix to the right side of A, thereby producing a matrix of the form [A | I]. Then we should apply row opperations to this matrix until the left side is reduced to I. This opperations will convert the right side to A-1, so the final matrix will have the form [I |A-1 ].(There are many other methods how to find the inverse of a n x n matrix, but I can't show them by examples. I am so sorry that I can't be so much useful to you).
Find the additive inverse of 9?
9
How do you find the additive inverse of an integer?
Change its sign.
