Maths-
General
Easy
Question
Let A =
. If U1, U2, U3 are column matrices satisfying AU1 =
, AU2 =
, AU3 =
and U is 3 × 3 matrix whose columns are U1, U2 and U3. Then |U| =
- 3
- 3/2
- –3
- 2
The correct answer is: 3
U1 =
, U2 =
, U3 = ![open square brackets table row cell a subscript 3 end subscript end cell row cell b subscript 3 end subscript end cell row cell c subscript 3 end subscript end cell end table close square brackets](data:image/png;base64,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)
A. U1 = ![open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell 1 0 0 end cell row cell 2 1 0 end cell row cell 3 2 1 end cell end table close square brackets](data:image/png;base64,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)
= ![open square brackets table row 1 row 0 row 0 end table close square brackets](data:image/png;base64,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)
=
=![open square brackets table row 1 row 0 row 0 end table close square brackets](data:image/png;base64,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)
a1 = 1, b1 = –2, c1 = 1
U1 = ![open square brackets table row 1 row cell – 2 end cell row 1 end table close square brackets](data:image/png;base64,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)
Similarly U2 =
& U3 = ![open square brackets table row 2 row cell – 1 end cell row cell – 3 end cell end table close square brackets](data:image/png;base64,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)
U =
|U| = 3
Related Questions to study
maths-
If the matrix A =
is singular, then λ equal to -
If the matrix A =
is singular, then λ equal to -
maths-General
maths-
If AB = I and B = A' then :
If AB = I and B = A' then :
maths-General
maths-
If A and B are square matrices of same size and |B|
0, then (B–1 AB)4 =
If A and B are square matrices of same size and |B|
0, then (B–1 AB)4 =
maths-General
maths-
If B is non-singular matrix and A is a square matrix of same size, then det (B–1 AB) =
If B is non-singular matrix and A is a square matrix of same size, then det (B–1 AB) =
maths-General
maths-
If A satisfies the equation x3 – 5x2 + 4x + k = 0, then A–1 exists if -
If A satisfies the equation x3 – 5x2 + 4x + k = 0, then A–1 exists if -
maths-General
Maths-
If 3A =
and A is orthogonal, then x + y =
If 3A =
and A is orthogonal, then x + y =
Maths-General
maths-
If A, B are symmetric matrices of the same order then (AB – BA) is -
If A, B are symmetric matrices of the same order then (AB – BA) is -
maths-General
maths-
If A =
is symmetric, then x =
If A =
is symmetric, then x =
maths-General
Maths-
If the rank of the matrix
is 2 then
If the rank of the matrix
is 2 then
Maths-General
Maths-
If A =
, then AT + A = I2, if –
If A =
, then AT + A = I2, if –
Maths-General
maths-
If A =
and B =
, then value of
for which A2 = B is:
If A =
and B =
, then value of
for which A2 = B is:
maths-General
chemistry-
Which of the following has no action with starch solution?
Which of the following has no action with starch solution?
chemistry-General
Maths-
Let three matrices A =
; B =
and C =
then tr(A) + tr
+ tr
+ tr
+ ....... +
=
Let three matrices A =
; B =
and C =
then tr(A) + tr
+ tr
+ tr
+ ....... +
=
Maths-General
Maths-
A =
then let us define a function f(x) = dt.(ATA–1) then which of the following can not be the value of
is (n ≥ 2)
A =
then let us define a function f(x) = dt.(ATA–1) then which of the following can not be the value of
is (n ≥ 2)
Maths-General
Maths-
Let A, B, C, D be (not necessarily square) real matrices such that AT = BCD; BT = CDA; CT = DAB and DT = ABC for the matrix S = ABCD, consider the two statements.
I. S3 = S
II. S2 = S4
Let A, B, C, D be (not necessarily square) real matrices such that AT = BCD; BT = CDA; CT = DAB and DT = ABC for the matrix S = ABCD, consider the two statements.
I. S3 = S
II. S2 = S4
Maths-General