Given the following vector X, find anon zero square marix A such that AX=0; You can resize a matrix by clicking and dragging the bottom-right corner of the matrix. X=[86−7] A=[000000000]

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Given the following vector X, find anon zero square marix A such that AX=0;  You can resize a matrix by clicking and dragging the bottom-right corner of the matrix.  X=[86−7]  A=[000000000]

Squairron · Accepted Answer

Definition used -&amp;nbsp;Product of two matrices -&amp;nbsp;If the number of rows in the second matrix equals the number of columns in the first matrix, then the product of the two matrices is possible.The corresponding column element from the second matrix and the row element from the first matrix were multiplied and added.Given:&amp;nbsp;X=[86−7]&amp;nbsp;Let&amp;nbsp;A=[abcdefghi]&amp;nbsp;Here a, b, c, d, e, f, g, and h are non-zero.&amp;nbsp;AX=0&amp;nbsp;[abcdefghi]&amp;nbsp;8a+6b−7c=0&amp;nbsp;8d+6e−7f=0&amp;nbsp;8g+6h−7i=0&amp;nbsp;Therefore, we must select any three numbers that stabilize these equations.a=1,b=1&amp;nbsp;and&amp;nbsp;c=2&amp;nbsp;will stsify this equation&amp;nbsp;So we can write matrix-&amp;nbsp;A=[112−1−1−2224]

Nick Camelot · Accepted Answer

Step 1: Let&#039;s assume A = [abcdefghi].Now, we need to solve the equation AX = 0. Multiplying the matrices, we get:[abcdefghi][86−7]=[8a+6b−7c8d+6e−7f8g+6h−7i]=[000].We need to find non-zero values for a, b, c, d, e, f, g, h, and i such that the resulting matrix is zero.From the first row of the resulting matrix, we have the equation 8a + 6b - 7c = 0.From the second row, we have the equation 8d + 6e - 7f = 0.From the third row, we have the equation 8g + 6h - 7i = 0.Step 2: To simplify the problem, let&#039;s choose a value of 1 for a and solve for the remaining variables.Using a = 1, we have the equations:8 + 6b - 7c = 0,8d + 6e - 7f = 0,8g + 6h - 7i = 0.Solving these equations, we find the following values:b = 7/6,c = 8/7,d = -6e/7,f = 8d/7,g = -6h/7,i = 8g/7.Thus, a possible non-zero square matrix A that satisfies AX = 0 is:A=[17/68/7−6e/7e8d/7−6h/7h8g/7].

Mr Solver · Accepted Answer

To find a non-zero square matrix A such that AX=0, where X is given as X=[86−7] and A is given as A=[000000000], we can multiply the matrices together using matrix multiplication.The matrix equation AX=0 can be written as AX=[000000000][86−7]=0.Performing the matrix multiplication, we get:AX=[000000000][86−7]=[0·8+0·6+0·(−7)0·8+0·6+0·(−7)0·8+0·6+0·(−7)]=[000]=0.Since the result is the zero vector [000], we can see that the given matrix A satisfies the equation AX=0.

Given the following vector X, find anon zero square marix

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