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If A=[■(-2&0&0@0&-2&0@0&0&-2)]. Find |adj A|.

If A is a square matrix of order 3 such that A(adj A)=10I. Then find |adj A|.

Find the matrix ‘X’ so that X×[■(1&2&3@4&5&6)]=[■(-7&-8&-9@2&4&6)]

If F(x)=[■(cos⁡x&-sin⁡x&0@sin⁡x&cos⁡x&0@0&0&1)], show that F(x)⋅F(y)=F(x+y).

Find the matrix A satisfying the matrix equation [■(2&1@3&2)]A[■(-3&2@5&-3)]=[■(1&0@0&1)].

If A=[■(3&1@-1&2)], show that A^2-5A+7I_2=O. Hence find A^(-1).

If A=[■(0&-tan⁡〖α/2〗@tan⁡〖α/2〗&0)] & I is the identity matrix of order 2, show that I+A=(I -A)......

If A=[■(cos⁡2θ&sin⁡2θ@-sin⁡2θ&cos⁡2θ )], find A^2.

Let A=[■(2&3@-1&2)] and f(x)=x^2-4x+7. Show that f(A)=O. Use this result to find A^5.

If A=[■(-3&2@1&-1)] & I=[■(1&0@0&1)]. Find k so that A^2+I=kA.

CONCEPT: PROPERTIES OF INVERSE OF A MATRIX

CONCEPT: PROPERTIES OF ADJOINT OF A MATRIX

CONCEPT: MATRIX MULTIPLICATION

In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how.....

At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment.....

Find the general solution: e^x tan⁡y dx+(1-e^x ) sec^2⁡y dy=0

Find the general solution: y log⁡y dx-x dy=0

Find the general solution: sec^2⁡x tan⁡x dx+sec^2⁡y tan⁡x dy=0

Find the general solution: dy/dx=(1-cos⁡x)/(1+cos⁡x )

COMPLETE EXERCISE 7.5 | ONE SHOT VIDEO

Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinat...

Find general solution: x log⁡x dy/dx+y=2/x log⁡x

Find the particular solution of the differential equation dx/dy+y cot⁡x=2x+x^2 cot⁡x (x≠0)........

Find the general solution of the differential equation ydx-(x+2y^2 )dy=0