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Find the value of lambda, a non-zero sca...

Find the value of `lambda,` a non-zero scalar, if `lambda[(1 ,0, 2),( 3,4, 5)]+2[(1,2,3),(-1,-3,2)]=[(4, 4, 10),( 4, 2 ,14)]`

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To find the value of \( \lambda \) in the equation \[ \lambda \begin{pmatrix} 1 & 0 & 2 \\ 3 & 4 & 5 \end{pmatrix} + 2 \begin{pmatrix} 1 & 2 & 3 \\ -1 & -3 & 2 \end{pmatrix} = \begin{pmatrix} 4 & 4 & 10 \\ 4 & 2 & 14 \end{pmatrix}, \] we will follow these steps: ...
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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
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  2. If matrix A=[a(ij)](2X2), where a(ij)={[1,i!=j],[0,i=j]}, then A^2 i...

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  3. Find the value of lambda, a non-zero scalar, if lambda[(1 ,0, 2),( 3,4...

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  4. Solve the matrix equation [(x^2),(y^2)]-3[(x),(2y)]=[(-2) ,(9)]

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  9. If A=[[ 2, -1],[3 , 1]] and B=[[1, 4],[7, 2]], find 3A-2B

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  13. Let A ,B be two matrices such that they commute. Show that for any pos...

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  14. Let A=[[2,3],[-1,2]] and f(x)=x^2-4x+7 Show that f(A)=0 Use this resul...

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  16. If A is a square matrix such that A^2=A , show that (I+A)^3=7A+Idot

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  17. Under what conditions is the matrix A^2-B^2=(A-B)(A+B) is true?

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  18. If a is a non-zero real or complex number. Use the principle of mathe...

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  19. If A = [[cos^2theta, costhetasintheta],[costhetasintheta, sin^2theta]]...

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  20. If A and B are square matrices of order n , then prove that A \ a n d ...

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