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Find the values of $\lambda$ for which the following equations have a solution and solve them completely for each value of $\lambda $ .
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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what values of $\lambda$, system of equations have a non-trivial solution? Obtain solution for real values of $\lambda$ where $3x+y-\lambda z=0 \; ; 4x-2y-3z=0 \; ; 2\lambda +4y-\lambda z =0$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Determine the values of $\lambda $ so that the equations $x+y+z=1 \; ; \; x+2y+4z=\lambda \; ; \; x+4y+10z=\lambda^2$ have solution and solve them completely in each case.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Reduce the matrix A to normal form and hence find its rank where $ A \;=\;\left[ \begin{array}{cccc}0& 1& -3& -1\\1& 0& 4& 3\\3& 1& 0& 2 \\1& 1& -2& 0\end{array}\right] $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Test the consistency of the following equations and solve them if they are consistent $ \\ \; \\ 2x-y+z=8 \; , \; 3x-y+z=6 \;, \; 4x-y+2z=7 \;, \; -x+y-z=4 $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Reduce the matrix A to normal form and hence find its rank where $ \left[ \begin{array}{cccc}1&-1& 3& 6\\1& 3&-3 &-4\\5& 3 & 3 & 11\end{array}\right] $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Prove that $sinh \; x \; = \; x+\dfrac{x^3}{3!}+\dfrac{x^5}{5!}+\dfrac{x^7}{7!}+\ldots $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Show that every square matrix can be uniquely expressed as the sum of Hermitian and skew Hermitian matrix.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If 'A' is Skew Symmetric matrix of odd order, then prove that it is singular.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find two non-singular matrices P & Q such that PAQ is in normal form where$ A= \left[ \begin{array}{cccc} 1 & 2 & 3 & -4 \\ 2 & 1 & 4 & -5 \\ -1 & -5 & -5 & 7 \end{array}\right]$ Also find rank of A
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Reduce matrix A to normal form and find its rank where $A=\left[ \begin{array}{cccc} 1 & 2 & 3 & 2 \\ 2 & 3 & 5 & 1 \\ 1 & 3 & 4 & 5 \end{array} \right] $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Reduce the following matrix into normal form and find its rank. $\left[ \begin{array}{ccc} 2 & -1 & 1 & 1\\ 1 & 0 & 1 & 2 \\ 3 & 3 & 3 & 1 \\ 1 & 4 & 2 & 0 \\ 0 & -4 & -1 & -2 \end{array}\right]$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Express the relation in $\alpha,\beta,\gamma,\delta \; for \; which \;A\;= \;\left[ \begin{array}{ccc}\alpha+i\gamma & -\beta+i\delta\\ \beta+i\delta & \alpha-i\gamma\end{array} \right] $is Unitary.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the value of a, b, c and $A^{-1}$ when $A = \dfrac 19 \begin{vmatrix} -8 & 4& a\\ 1&4&b\\ 4&7&c\\ \end{vmatrix}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the rank of the matrix by reducing it to normal form $\begin{vmatrix} 1&1&1\\ 1&-1&-1\\ 3&1&1\\ \end{vmatrix} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find non-singular matrices P and Q such that $A =\begin{vmatrix} 1&2&3&4\\ 2&1&4&3\\ 3&0&5&-10\\ \end{vmatrix}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Test for consistency and solve if consistent
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Examine whether the vectors $X_1 = [3,1,1] , X_2=[2,0,-1] X_3 = [4,2,1]$ are Linearly independent
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $A=\begin{vmatrix} 1&2&-2\\ -1&3&0\\ 0&-2&1\\ \end{vmatrix}$ then find two non singular matrices P & Q. Such that PAQ is in normal form. Also find P(A) and $A^{-1}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Show that the vectors are linearly dependent & Find the relation between them - $X_1$ =[1,2,1,0] ; $X_2$=[1,3,1,2] ; $X_3$ =[4,2,1,0] ; $X_4$ = [6,1,0,1]
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Examine the following vectors for linear dependence/ independence : $X_1$=(a,b,c) , $X_2$=(b,c,a) ; $X_3$=(c,a,b) where a+b+c $\ne$ 0
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Examine whether vectors $x_1=[3,1,1],x_2=[2,0,-1],x_3=[4,2,1]$ are linearly independent.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Determine linear dependence or independence of vectors $x_1=[1,3,4,2], \; x_2=[3,-5,2,6], \; x_3=[2,-1,3,4]. $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Express the matrix A as a sum of Hermitian and skew Hermitian matrix where $ \left[ \begin{array}{ccc}3i & -1+i & 3-2i\\1+i & -i & 1+2i \\-3-2i & -1+2i & 0\end{array} \right] $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the $n^{th}$ derivative of $ y=sinx \;sin2x \;sin3x$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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