Matrix

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #111

If $ A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 3 & -1 \\ -1 & 1 & -7 \end{bmatrix}$ find `A^{-1}`. Hence solve the following equations. `x+y-z=3`, `2x+3y+z=10`, `3x-y-7z=1`

Question No: #112

From the matrix equation `AX=B` find the matrix `X`, given that $ A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1 \end{bmatrix} $ and $ B = \begin{bmatrix} 2 \\ 1 \\ 7 \end{bmatrix}$

Question No: #113

Find the matrix `A` where $ \begin{bmatrix} 2 & -1 \\ 1 & 0 \\ -3 & 4 \end{bmatrix} A = \begin{bmatrix} -1 & -8 & -10 \\ 1 & -2 & -5 \\ 9 & 22 & 15 \end{bmatrix} $

Question No: #114

Solve by using inverse matrix method. `x+2y+z=7`, `x+3z=11`, `2x-y=1`

Question No: #115

Solve by using inverse matrix method. `2x+3y+5z=5`, `x-2y+z=-4`, `3x-y-2z=3`

Question No: #116

Solve by using inverse matrix method. `2/x-3/y+3/z=10`, `1/x+1/y+1/z=10`, `3/x-1/y+2/z=13`

Question No: #117

By using the matrix method, show that the following set of equations have an infinite number of solutions. `x+2y+3z=1`, `3x+4y+5z=2`, `5x+6y+7z=3`

Question No: #118

Given $ A = \begin{bmatrix} 1 & -1 & 1 \\ 1 & -2 & -2 \\ 2 & 1 & 3 \end{bmatrix} $ and $ B = \begin{bmatrix} -4 & 4 & 4 \\ -7 & 1 & 3 \\ 5 & -3 & -1 \end{bmatrix} $. Find `AB`. Hence from this result, solve the following set of equations. `x-y+z=4`, `x-2y-2z=9`, `2x+y+3z=1`
Ans: `x=3, y=-2, z=-1`
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Question No: #119

Find the inverse of the following matrix by using elementary row transformations. $ \begin{pmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{pmatrix} $

Question No: #120

Find the inverse of the following matrix by using Elementary row operations. $ \begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 7 \\ -2 & -4 & -5 \end{bmatrix} $