Matrix

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

Click on each question to see answer & solution.

Question No: #101

If $ A = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} $ and `f(x) = x^3-6x^2+7x+2`, then show that `A` is a root of `f(x)=0`
Ans: N.A.
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Question No: #102

Show that the matrix $ P = \frac{1}{3}\begin{pmatrix} -1 & 2 & -2 \\ -2 & 1 & 2 \\ 2 & 2 & 1 \end{pmatrix}$ is proper orthogonal, and hence find `P^{-1}`
Ans: `P^{-1} = P^T` $ = \frac{1}{3}\begin{pmatrix} -1 & -2 & 2 \\ 2 & 1 & 2 \\ -2 & 2 & 1 \end{pmatrix}$
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Question No: #103

Show that the matrix $ \begin{pmatrix} 3 & 2 & 1 \\ 0 & 4 & 5 \\ 3 & 6 & 6 \end{pmatrix} $ is non-singular.

Question No: #104

If `|A|=2` and $ Adj(A) = \begin{bmatrix} -2 & 3 & 1 \\ 6 & -8 & -2 \\ -4 & 7 & 2 \end{bmatrix} $ then find the matrix `A`

Question No: #105

If $ A = \begin{bmatrix} 1 & 0 & 2 \\ 3 & 4 & -1 \\ 0 & 5 & 6 \end{bmatrix} $ then show that `(A^T)^{-1} = (A^{-1})^T`.

Question No: #106

If $ A =\frac{1}{9} \begin{bmatrix} -8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & -8 & 4 \end{bmatrix} $ , then show that `A^{-1} = A^T`.

Question No: #107

If $ A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & -1 & 0 \\ 1 & 0 & 0 \end{bmatrix} $ then show that `A^2 = A^{-1}`. Hence find `A^3`

Question No: #108

If $ A = \begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{bmatrix} $ then verify the relation `A\cdot(adj\ A) = |A|\cdot I`. Hence find `A^{-1}`

Question No: #109

If $ A = \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix}$ then find `A^{-1}` and also show that `A\A^{-1} = A^{-1}A = I`

Question No: #110

If $ A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} $ then find `A^{-1}`. Hence solve the following equations. `2x-3y+5z=11`, `3x+2y-4z=-5`, `x+y-2z=-3`