Find x such that the matrix is equal to its inverse.A=[7x−8−7]

Question

Find x such that the matrix is ​​equal to its inverse.A=[7x−8−7]

Luvottoq · Accepted Answer

Step 1 Given matrix, A=[7x−8−7] And, A=A−1 Formula for an inverse of a matrix is A−1=1detAadjA Step 2 Now, det(A)=7(−7)−x(−8) det(A)=−49+8x det(A)=8x−49 And, adjA=[−7−x87] so, A−1=[−78x−49−x8x−4988x−4978x−49] Step 3 Now , as given A=A−1 [7x−8−7]=[−78x−49−x8x−4988x−4978x−49] on comparing the matrices, 7=78x−49 7(8x−49)=−7 56x−343=−7 56x=343−7 56x=343−7 56x=336 x=33656 x=6 Step 4 Therefore, The value of x such that the matrix is equal to its own inverse is x=6

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Eliza Beth13 · Accepted Answer

Answer:7=−7−49+8x and x=−x−49+8xExplanation:Let&#039;s represent the given matrix A as:A=[7x−8−7]To find the inverse of A, we can use the formula for a 2x2 matrix:A−1=1det(A)[d−b−ca]where det(A) represents the determinant of A, and a, b, c, and d are the elements of the matrix A.The determinant of A can be calculated as:det(A)=ad−bcIn this case, we have:a=7,b=x,c=−8,d=−7Substituting the values into the determinant formula, we get:det(A)=(7·−7)−(x·−8)Simplifying further:det(A)=−49+8xFor A to be equal to its inverse, we need to set A equal to its inverse and solve for x. This gives us the following equation:[7x−8−7]=1−49+8x[−7−x87]To find x, we can equate the corresponding elements of the matrices:7=−7−49+8xandx=−x−49+8xSolving these equations will give us the value(s) of x that satisfy the condition.7=−7−49+8x and x=−x−49+8x

Mr Solver · Accepted Answer

Step 1: Calculating the inverse of matrix A:A−1=1det(A)[d−b−ca]where a, b, c, and d are the entries of matrix A.To find det(A), we can use the formula:det(A)=ad−bcSubstituting the values from matrix A:det(A)=(7)(−7)−(x)(−8)=−49+8xNow we can substitute the values of a, b, c, and d into the formula for A−1:A−1=1−49+8x[−7−x87]Step 2: Equating A and A−1:A=A−1Substituting the matrices:[7x−8−7]=1−49+8x[−7−x87]Step 3: Solving for x:Now we can equate the corresponding elements of the matrices and solve for x.For the top left element:7=−7−49+8xFor the top right element:x=−x−49+8xSimplifying these equations gives us:49=−78x=−8xThese equations are not possible to satisfy. Hence, there is no solution for x that makes matrix A equal to its inverse.

madeleinejames20 · Accepted Answer

To find x such that the matrix A is equal to its inverse, we can set up the equation as follows:A=A−1Given matrix A:A=[7x−8−7]Let&#039;s find the inverse of matrix A:A−1=1ad−bc[d−b−ca]where a, b, c, and d are the elements of matrix A. Plugging in the values:A−1=1(7)(−7)−(x)(−8)[−7−x87]Simplifying the determinant:(7)(−7)−(x)(−8)=49+8xTo find x such that A is equal to its inverse, we equate the matrices:[7x−8−7]=149+8x[−7−x87]Now, we can equate the corresponding elements of the matrices:7=−749+8xx=−x49+8x−8=849+8x−7=749+8xSolving these equations will give us the value of x.

Find x such that the matrix is equal to its own inverse. A=begin{bmatrix}7 & x -8 & -7 end{bmatrix}

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